Merge branch 'main' into next

2026-08-14 08:03:11 +00:00 · 2023-09-11 23:09:20 +02:00 · 2023-09-11 20:00:02 +02:00 · 2023-09-11 13:14:18 +02:00 · 2023-09-11 10:52:01 +00:00 · 2023-09-11 12:31:34 +02:00
203 changed files with 27915 additions and 23530 deletions
@@ -0,0 +1,290 @@
+---
+kind: pipeline
+name: default
+
+node:
+  nix-daemon: 1
+
+steps:
+  - name: check formatting
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-shell --attr rust --run "cargo fmt -- --check"
+
+  - name: build
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-build --no-build-output --attr clippy.amd64 --argstr git_version ${DRONE_TAG:-$DRONE_COMMIT}
+
+  - name: unit + func tests
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      GARAGE_TEST_INTEGRATION_EXE: result-bin/bin/garage
+      GARAGE_TEST_INTEGRATION_PATH: tmp-garage-integration
+    commands:
+      - nix-build --no-build-output --attr clippy.amd64 --argstr git_version ${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-build --no-build-output --attr test.amd64
+      - ./result/bin/garage_db-*
+      - ./result/bin/garage_api-*
+      - ./result/bin/garage_model-*
+      - ./result/bin/garage_rpc-*
+      - ./result/bin/garage_table-*
+      - ./result/bin/garage_util-*
+      - ./result/bin/garage_web-*
+      - ./result/bin/garage-*
+      - ./result/bin/integration-* || (cat tmp-garage-integration/stderr.log; false)
+      - rm result
+      - rm -rv tmp-garage-integration
+
+  - name: integration tests
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-build --no-build-output --attr clippy.amd64 --argstr git_version ${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr integration --run ./script/test-smoke.sh || (cat /tmp/garage.log; false)
+
+trigger:
+  event:
+  - custom
+  - push
+  - pull_request
+  - tag
+  - cron
+
+---
+kind: pipeline
+type: docker
+name: release-linux-amd64
+
+node:
+  nix-daemon: 1
+
+steps:
+  - name: build
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-build --no-build-output --attr pkgs.amd64.release --argstr git_version ${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr rust --run "./script/not-dynamic.sh result-bin/bin/garage"
+
+  - name: integration
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-shell --attr integration --run ./script/test-smoke.sh || (cat /tmp/garage.log; false)
+
+  - name: push static binary
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      AWS_ACCESS_KEY_ID:
+        from_secret: garagehq_aws_access_key_id
+      AWS_SECRET_ACCESS_KEY:
+        from_secret: garagehq_aws_secret_access_key
+      TARGET: "x86_64-unknown-linux-musl"
+    commands:
+      - nix-shell --attr release --run "to_s3"
+
+  - name: docker build and publish
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      DOCKER_AUTH:
+        from_secret: docker_auth
+      DOCKER_PLATFORM: "linux/amd64"
+      CONTAINER_NAME: "dxflrs/amd64_garage"
+      HOME: "/kaniko"
+    commands:
+      - mkdir -p /kaniko/.docker
+      - echo $DOCKER_AUTH > /kaniko/.docker/config.json
+      - export CONTAINER_TAG=${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr release --run "to_docker"
+
+
+trigger:
+  event:
+  - promote
+  - cron
+
+---
+kind: pipeline
+type: docker
+name: release-linux-i386
+
+node:
+  nix-daemon: 1
+
+steps:
+  - name: build
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-build --no-build-output --attr pkgs.i386.release --argstr git_version ${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr rust --run "./script/not-dynamic.sh result-bin/bin/garage"
+
+  - name: integration
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-shell --attr integration --run ./script/test-smoke.sh || (cat /tmp/garage.log; false)
+
+  - name: push static binary
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      AWS_ACCESS_KEY_ID:
+        from_secret: garagehq_aws_access_key_id
+      AWS_SECRET_ACCESS_KEY:
+        from_secret: garagehq_aws_secret_access_key
+      TARGET: "i686-unknown-linux-musl"
+    commands:
+      - nix-shell --attr release --run "to_s3"
+
+  - name: docker build and publish
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      DOCKER_AUTH:
+        from_secret: docker_auth
+      DOCKER_PLATFORM: "linux/386"
+      CONTAINER_NAME: "dxflrs/386_garage"
+      HOME: "/kaniko"
+    commands:
+      - mkdir -p /kaniko/.docker
+      - echo $DOCKER_AUTH > /kaniko/.docker/config.json
+      - export CONTAINER_TAG=${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr release --run "to_docker"
+
+trigger:
+  event:
+  - promote
+  - cron
+
+---
+kind: pipeline
+type: docker
+name: release-linux-arm64
+
+node:
+  nix-daemon: 1
+
+steps:
+  - name: build
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-build --no-build-output --attr pkgs.arm64.release --argstr git_version ${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr rust --run "./script/not-dynamic.sh result-bin/bin/garage"
+
+  - name: push static binary
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      AWS_ACCESS_KEY_ID:
+        from_secret: garagehq_aws_access_key_id
+      AWS_SECRET_ACCESS_KEY:
+        from_secret: garagehq_aws_secret_access_key
+      TARGET: "aarch64-unknown-linux-musl"
+    commands:
+      - nix-shell --attr release --run "to_s3"
+
+  - name: docker build and publish
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      DOCKER_AUTH:
+        from_secret: docker_auth
+      DOCKER_PLATFORM: "linux/arm64"
+      CONTAINER_NAME: "dxflrs/arm64_garage"
+      HOME: "/kaniko"
+    commands:
+      - mkdir -p /kaniko/.docker
+      - echo $DOCKER_AUTH > /kaniko/.docker/config.json
+      - export CONTAINER_TAG=${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr release --run "to_docker"
+
+trigger:
+  event:
+  - promote
+  - cron
+
+---
+kind: pipeline
+type: docker
+name: release-linux-arm
+
+node:
+  nix-daemon: 1
+
+steps:
+  - name: build
+    image: nixpkgs/nix:nixos-22.05
+    commands:
+      - nix-build --no-build-output --attr pkgs.arm.release --argstr git_version ${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr rust --run "./script/not-dynamic.sh result-bin/bin/garage"
+
+  - name: push static binary
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      AWS_ACCESS_KEY_ID:
+        from_secret: garagehq_aws_access_key_id
+      AWS_SECRET_ACCESS_KEY:
+        from_secret: garagehq_aws_secret_access_key
+      TARGET: "armv6l-unknown-linux-musleabihf"
+    commands:
+      - nix-shell --attr release --run "to_s3"
+
+  - name: docker build and publish
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      DOCKER_AUTH:
+        from_secret: docker_auth
+      DOCKER_PLATFORM: "linux/arm"
+      CONTAINER_NAME: "dxflrs/arm_garage"
+      HOME: "/kaniko"
+    commands:
+      - mkdir -p /kaniko/.docker
+      - echo $DOCKER_AUTH > /kaniko/.docker/config.json
+      - export CONTAINER_TAG=${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr release --run "to_docker"
+
+trigger:
+  event:
+  - promote
+  - cron
+
+---
+kind: pipeline
+type: docker
+name: refresh-release-page
+
+node:
+  nix-daemon: 1
+
+steps:
+  - name: multiarch-docker
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      DOCKER_AUTH:
+        from_secret: docker_auth
+      HOME: "/root"
+    commands:
+      - mkdir -p /root/.docker
+      - echo $DOCKER_AUTH > /root/.docker/config.json
+      - export CONTAINER_TAG=${DRONE_TAG:-$DRONE_COMMIT}
+      - nix-shell --attr release --run "multiarch_docker"
+  - name: refresh-index
+    image: nixpkgs/nix:nixos-22.05
+    environment:
+      AWS_ACCESS_KEY_ID:
+        from_secret: garagehq_aws_access_key_id
+      AWS_SECRET_ACCESS_KEY:
+        from_secret: garagehq_aws_secret_access_key
+    commands:
+      - mkdir -p /etc/nix && cp nix/nix.conf /etc/nix/nix.conf
+      - nix-shell --attr release --run "refresh_index"
+
+depends_on:
+  - release-linux-amd64
+  - release-linux-i386
+  - release-linux-arm64
+  - release-linux-arm
+
+trigger:
+  event:
+  - promote
+  - cron
+
+---
+kind: signature
+hmac: 24aebbcdba84fd0cdf963061d7bb72ae5b915bfdd0f50c7b019001126fb7fa56
+
+...
@@ -1,44 +0,0 @@
-when:
-  event:
-  - push
-  - tag
-  - pull_request
-  - deployment
-  - cron
-
-steps:
-  - name: check formatting
-    image: nixpkgs/nix:nixos-22.05
-    commands:
-      - nix-shell --attr rust --run "cargo fmt -- --check"
-
-  - name: build
-    image: nixpkgs/nix:nixos-22.05
-    commands:
-      - nix-build --no-build-output --attr clippy.amd64 --argstr git_version ${CI_COMMIT_TAG:-$CI_COMMIT_SHA}
-
-  - name: unit + func tests
-    image: nixpkgs/nix:nixos-22.05
-    environment:
-      GARAGE_TEST_INTEGRATION_EXE: result-bin/bin/garage
-      GARAGE_TEST_INTEGRATION_PATH: tmp-garage-integration
-    commands:
-      - nix-build --no-build-output --attr clippy.amd64 --argstr git_version ${CI_COMMIT_TAG:-$CI_COMMIT_SHA}
-      - nix-build --no-build-output --attr test.amd64
-      - ./result/bin/garage_db-*
-      - ./result/bin/garage_api-*
-      - ./result/bin/garage_model-*
-      - ./result/bin/garage_rpc-*
-      - ./result/bin/garage_table-*
-      - ./result/bin/garage_util-*
-      - ./result/bin/garage_web-*
-      - ./result/bin/garage-*
-      - ./result/bin/integration-* || (cat tmp-garage-integration/stderr.log; false)
-      - rm result
-      - rm -rv tmp-garage-integration
-
-  - name: integration tests
-    image: nixpkgs/nix:nixos-22.05
-    commands:
-      - nix-build --no-build-output --attr clippy.amd64 --argstr git_version ${CI_COMMIT_TAG:-$CI_COMMIT_SHA}
-      - nix-shell --attr integration --run ./script/test-smoke.sh || (cat /tmp/garage.log; false)
@@ -1,29 +0,0 @@
-when:
-  event:
-  - deployment
-  - cron
-
-depends_on:
-  - release
-
-steps:
-  - name: refresh-index
-    image: nixpkgs/nix:nixos-22.05
-    secrets:
-      - source: garagehq_aws_access_key_id
-        target: AWS_ACCESS_KEY_ID
-      - source: garagehq_aws_secret_access_key
-        target: AWS_SECRET_ACCESS_KEY
-    commands:
-      - mkdir -p /etc/nix && cp nix/nix.conf /etc/nix/nix.conf
-      - nix-shell --attr release --run "refresh_index"
-
-  - name: multiarch-docker
-    image: nixpkgs/nix:nixos-22.05
-    secrets:
-      - docker_auth
-    commands:
-      - mkdir -p /root/.docker
-      - echo $DOCKER_AUTH > /root/.docker/config.json
-      - export CONTAINER_TAG=${CI_COMMIT_TAG:-$CI_COMMIT_SHA}
-      - nix-shell --attr release --run "multiarch_docker"
@@ -1,66 +0,0 @@
-when:
-  event:
-  - deployment
-  - cron
-
-matrix:
-  include:
-    - ARCH: amd64
-      DOCKER_ARCH: amd64
-      TARGET: x86_64-unknown-linux-musl
-    - ARCH: i386
-      DOCKER_ARCH: "386"
-      TARGET: i686-unknown-linux-musl
-    - ARCH: arm64
-      DOCKER_ARCH: arm64
-      TARGET: aarch64-unknown-linux-musl
-    - ARCH: arm
-      DOCKER_ARCH: arm
-      TARGET: armv6l-unknown-linux-musleabihf
-
-steps:
-  - name: build
-    image: nixpkgs/nix:nixos-22.05
-    commands:
-      - nix-build --no-build-output --attr pkgs.${ARCH}.release --argstr git_version ${CI_COMMIT_TAG:-$CI_COMMIT_SHA}
-
-  - name: check is static binary
-    image: nixpkgs/nix:nixos-22.05
-    commands:
-      - nix-build --no-build-output --attr pkgs.${ARCH}.release --argstr git_version ${CI_COMMIT_TAG:-$CI_COMMIT_SHA}
-      - nix-shell --attr rust --run "./script/not-dynamic.sh result-bin/bin/garage"
-
-  - name: integration tests
-    image: nixpkgs/nix:nixos-22.05
-    commands:
-      - nix-shell --attr integration --run ./script/test-smoke.sh || (cat /tmp/garage.log; false)
-    when:
-      - matrix:
-          ARCH: amd64
-      - matrix:
-          ARCH: i386
-
-  - name: push static binary
-    image: nixpkgs/nix:nixos-22.05
-    environment:
-      TARGET: "${TARGET}"
-    secrets:
-      - source: garagehq_aws_access_key_id
-        target: AWS_ACCESS_KEY_ID
-      - source: garagehq_aws_secret_access_key
-        target: AWS_SECRET_ACCESS_KEY
-    commands:
-      - nix-shell --attr release --run "to_s3"
-
-  - name: docker build and publish
-    image: nixpkgs/nix:nixos-22.05
-    environment:
-      DOCKER_PLATFORM: "linux/${DOCKER_ARCH}"
-      CONTAINER_NAME: "dxflrs/${DOCKER_ARCH}_garage"
-    secrets:
-      - docker_auth
-    commands:
-      - mkdir -p /root/.docker
-      - echo $DOCKER_AUTH > /root/.docker/config.json
-      - export CONTAINER_TAG=${CI_COMMIT_TAG:-$CI_COMMIT_SHA}
-      - nix-shell --attr release --run "to_docker"
@@ -119,18 +119,6 @@ version = "1.6.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "bddcadddf5e9015d310179a59bb28c4d4b9920ad0f11e8e14dbadf654890c9a6"

-[[package]]
-name = "argon2"
-version = "0.5.3"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3c3610892ee6e0cbce8ae2700349fcf8f98adb0dbfbee85aec3c9179d29cc072"
-dependencies = [
- "base64ct",
- "blake2",
- "cpufeatures",
- "password-hash",
-]
-
 [[package]]
 name = "arrayvec"
 version = "0.5.2"
@@ -609,12 +597,6 @@ dependencies = [
 "vsimd",
 ]

-[[package]]
-name = "base64ct"
-version = "1.6.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8c3c1a368f70d6cf7302d78f8f7093da241fb8e8807c05cc9e51a125895a6d5b"
-
 [[package]]
 name = "bincode"
 version = "1.3.3"
@@ -808,9 +790,9 @@ checksum = "e496a50fda8aacccc86d7529e2c1e0892dbd0f898a6b5645b5561b89c3210efa"

 [[package]]
 name = "cpufeatures"
-version = "0.2.12"
+version = "0.2.9"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "53fe5e26ff1b7aef8bca9c6080520cfb8d9333c7568e1829cef191a9723e5504"
+checksum = "a17b76ff3a4162b0b27f354a0c87015ddad39d35f9c0c36607a3bdd175dde1f1"
 dependencies = [
 "libc",
 ]
@@ -1216,7 +1198,7 @@ dependencies = [

 [[package]]
 name = "garage"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
 "assert-json-diff",
 "async-trait",
@@ -1245,7 +1227,6 @@ dependencies = [
 "hyper",
 "k2v-client",
 "kuska-sodiumoxide",
- "mktemp",
 "netapp",
 "opentelemetry",
 "opentelemetry-otlp",
@@ -1268,9 +1249,8 @@ dependencies = [

 [[package]]
 name = "garage_api"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
- "argon2",
 "async-trait",
 "base64 0.21.3",
 "bytes",
@@ -1291,7 +1271,6 @@ dependencies = [
 "http-range",
 "httpdate",
 "hyper",
- "hyperlocal",
 "idna",
 "md-5",
 "multer",
@@ -1315,12 +1294,13 @@ dependencies = [

 [[package]]
 name = "garage_block"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
 "arc-swap",
 "async-compression",
 "async-trait",
 "bytes",
+ "bytesize",
 "futures",
 "futures-util",
 "garage_db",
@@ -1340,7 +1320,7 @@ dependencies = [

 [[package]]
 name = "garage_db"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
 "clap 4.4.0",
 "err-derive",
@@ -1355,12 +1335,13 @@ dependencies = [

 [[package]]
 name = "garage_model"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
 "arc-swap",
 "async-trait",
 "base64 0.21.3",
 "blake2",
+ "chrono",
 "err-derive",
 "futures",
 "futures-util",
@@ -1382,11 +1363,12 @@ dependencies = [

 [[package]]
 name = "garage_rpc"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
 "arc-swap",
 "async-trait",
 "bytes",
+ "bytesize",
 "err-derive",
 "futures",
 "futures-util",
@@ -1394,6 +1376,7 @@ dependencies = [
 "garage_util",
 "gethostname",
 "hex",
+ "itertools 0.10.5",
 "k8s-openapi",
 "kube",
 "kuska-sodiumoxide",
@@ -1414,7 +1397,7 @@ dependencies = [

 [[package]]
 name = "garage_table"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
 "arc-swap",
 "async-trait",
@@ -1436,7 +1419,7 @@ dependencies = [

 [[package]]
 name = "garage_util"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
 "arc-swap",
 "async-trait",
@@ -1470,7 +1453,7 @@ dependencies = [

 [[package]]
 name = "garage_web"
-version = "0.8.7"
+version = "0.8.4"
 dependencies = [
 "err-derive",
 "futures",
@@ -1480,10 +1463,8 @@ dependencies = [
 "garage_util",
 "http",
 "hyper",
- "hyperlocal",
 "opentelemetry",
 "percent-encoding",
- "tokio",
 "tracing",
 ]

@@ -1793,19 +1774,6 @@ dependencies = [
 "tokio-io-timeout",
 ]

-[[package]]
-name = "hyperlocal"
-version = "0.8.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0fafdf7b2b2de7c9784f76e02c0935e65a8117ec3b768644379983ab333ac98c"
-dependencies = [
- "futures-util",
- "hex",
- "hyper",
- "pin-project",
- "tokio",
-]
-
 [[package]]
 name = "iana-time-zone"
 version = "0.1.57"
@@ -2137,9 +2105,9 @@ checksum = "e2abad23fbc42b3700f2f279844dc832adb2b2eb069b2df918f455c4e18cc646"

 [[package]]
 name = "libc"
-version = "0.2.153"
+version = "0.2.147"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9c198f91728a82281a64e1f4f9eeb25d82cb32a5de251c6bd1b5154d63a8e7bd"
+checksum = "b4668fb0ea861c1df094127ac5f1da3409a82116a4ba74fca2e58ef927159bb3"

 [[package]]
 name = "libsodium-sys"
@@ -2634,17 +2602,6 @@ dependencies = [
 "regex",
 ]

-[[package]]
-name = "password-hash"
-version = "0.5.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "346f04948ba92c43e8469c1ee6736c7563d71012b17d40745260fe106aac2166"
-dependencies = [
- "base64ct",
- "rand_core",
- "subtle",
-]
-
 [[package]]
 name = "paste"
 version = "1.0.14"
@@ -18,14 +18,14 @@ default-members = ["src/garage"]

 [workspace.dependencies]
 format_table = { version = "0.1.1", path = "src/format-table" }
-garage_api = { version = "0.8.7", path = "src/api" }
-garage_block = { version = "0.8.7", path = "src/block" }
-garage_db = { version = "0.8.7", path = "src/db", default-features = false }
-garage_model = { version = "0.8.7", path = "src/model", default-features = false }
-garage_rpc = { version = "0.8.7", path = "src/rpc" }
-garage_table = { version = "0.8.7", path = "src/table" }
-garage_util = { version = "0.8.7", path = "src/util" }
-garage_web = { version = "0.8.7", path = "src/web" }
+garage_api = { version = "0.8.4", path = "src/api" }
+garage_block = { version = "0.8.4", path = "src/block" }
+garage_db = { version = "0.8.4", path = "src/db", default-features = false }
+garage_model = { version = "0.8.4", path = "src/model", default-features = false }
+garage_rpc = { version = "0.8.4", path = "src/rpc" }
+garage_table = { version = "0.8.4", path = "src/table" }
+garage_util = { version = "0.8.4", path = "src/util" }
+garage_web = { version = "0.8.4", path = "src/web" }
 k2v-client = { version = "0.0.4", path = "src/k2v-client" }

 [profile.dev]
@@ -37,7 +37,7 @@ Second, we suppose you have created a key and a bucket.
 As a reminder, you can create a key for your nextcloud instance as follow:

 ```bash
-garage key new --name nextcloud-key
+garage key create nextcloud-key
 ```

 Keep the Key ID and the Secret key in a pad, they will be needed later.  
@@ -139,7 +139,7 @@ a reasonable trade-off for some instances.
 Create a key for Peertube:

 ```bash
-garage key new --name peertube-key
+garage key create peertube-key
 ```

 Keep the Key ID and the Secret key in a pad, they will be needed later.  
@@ -253,7 +253,7 @@ As such, your Garage cluster should be configured appropriately for good perform
 This is the usual Garage setup:

 ```bash
-garage key new --name mastodon-key
+garage key create mastodon-key
 garage bucket create mastodon-data
 garage bucket allow mastodon-data --read --write --key mastodon-key
 ```
@@ -379,7 +379,7 @@ Supposing you have a working synapse installation, you can add the module with p
 Now create a bucket and a key for your matrix instance (note your Key ID and Secret Key somewhere, they will be needed later):

 ```bash
-garage key new --name matrix-key
+garage key create matrix-key
 garage bucket create matrix
 garage bucket allow matrix --read --write --key matrix-key
 ```
@@ -421,7 +421,7 @@ Now we can write a simple script (eg `~/.local/bin/matrix-cache-gc`):
 ## CONFIGURATION ##
 AWS_ACCESS_KEY_ID=GKxxx
 AWS_SECRET_ACCESS_KEY=xxxx
-AWS_ENDPOINT_URL=http://localhost:3900
+S3_ENDPOINT=http://localhost:3900
 S3_BUCKET=matrix
 MEDIA_STORE=/var/lib/matrix-synapse/media
 PG_USER=matrix
@@ -442,7 +442,7 @@ EOF

 s3_media_upload update-db 1d
 s3_media_upload --no-progress check-deleted $MEDIA_STORE
-s3_media_upload --no-progress upload $MEDIA_STORE $S3_BUCKET --delete --endpoint-url $AWS_ENDPOINT_URL
+s3_media_upload --no-progress upload $MEDIA_STORE $S3_BUCKET --delete --endpoint-url $S3_ENDPOINT
 ```

 This script will list all the medias that were not accessed in the 24 hours according to your database.
@@ -54,7 +54,7 @@ how to configure this.
 Create your key and bucket:

 ```bash
-garage key new my-key
+garage key create my-key
 garage bucket create backup
 garage bucket allow backup --read --write --key my-key
 ```
@@ -70,17 +70,16 @@ Then a file named `~/.aws/config` and put:
 ```toml
 [default]
 region=garage
-endpoint_url=http://127.0.0.1:3900
 ```

 Now, supposing Garage is listening on `http://127.0.0.1:3900`, you can list your buckets with:

 ```bash
-aws s3 ls
+aws --endpoint-url http://127.0.0.1:3900 s3 ls
 ```

-If you're using awscli `<1.29.0` or `<2.13.0`, you need to pass `--endpoint-url` to each CLI invocation explicitly.
-As a workaround, you can redefine the aws command by editing the file `~/.bashrc` in this case:
+Passing the `--endpoint-url` parameter to each command is annoying but AWS developers do not provide a corresponding configuration entry.
+As a workaround, you can redefine the aws command by editing the file `~/.bashrc`:

 ```
 function aws { command aws --endpoint-url http://127.0.0.1:3900 $@ ; }
@@ -23,7 +23,7 @@ You can configure a different target for each data type (check `[lfs]` and `[att
 Let's start by creating a key and a bucket (your key id and secret will be needed later, keep them somewhere):

 ```bash
-garage key new --name gitea-key
+garage key create gitea-key
 garage bucket create gitea
 garage bucket allow gitea --read --write --key gitea-key
 ```
@@ -118,7 +118,7 @@ through another support, like a git repository.
 As a first step, we will need to create a bucket on Garage and enabling website access on it:

 ```bash
-garage key new --name nix-key
+garage key create nix-key
 garage bucket create nix.example.com
 garage bucket allow nix.example.com --read --write --key nix-key
 garage bucket website nix.example.com --allow
@@ -75,16 +75,11 @@ to store 2 TB of data in total.

 - For the metadata storage, Garage does not do checksumming and integrity
  verification on its own. If you are afraid of bitrot/data corruption,
-  put your metadata directory on a BTRFS partition. Otherwise, just use regular
+  put your metadata directory on a ZFS or BTRFS partition. Otherwise, just use regular
  EXT4 or XFS.

- Having a single server with several storage drives is currently not very well
-  supported in Garage ([#218](https://git.deuxfleurs.fr/Deuxfleurs/garage/issues/218)).
-  For an easy setup, just put all your drives in a RAID0 or a ZFS RAIDZ array.
-  If you're adventurous, you can try to format each of your disk as
-  a separate XFS partition, and then run one `garage` daemon per disk drive,
-  or use something like [`mergerfs`](https://github.com/trapexit/mergerfs) to merge
-  all your disks in a single union filesystem that spreads load over them.
+- Servers with multiple HDDs are supported natively by Garage without resorting
+  to RAID, see [our dedicated documentation page](@/documentation/operations/multi-hdd.md).

 ## Get a Docker image

@@ -91,6 +91,16 @@ is definitely lost, then there is no other choice than to declare your S3 object
 as unrecoverable, and to delete them properly from the data store. This can be done
 using the `garage block purge` command.

+## Rebalancing data directories
+
+In [multi-HDD setups](@/documentation/operations/multi-hdd.md), to ensure that
+data blocks are well balanced between storage locations, you may run a
+rebalance operation using `garage repair rebalance`. This is usefull when
+adding storage locations or when capacities of the storage locations have been
+changed.  Once this is finished, Garage will know for each block of a single
+possible location where it can be, which can increase access speed.  This
+operation will also move out all data from locations marked as read-only.
+

 # Metadata operations

@@ -114,4 +124,3 @@ in your cluster, you can run one of the following repair procedures:

 - `garage repair versions`: checks that all versions belong to a non-deleted object, and purges any orphan version
 - `garage repair block_refs`: checks that all block references belong to a non-deleted object version, and purges any orphan block reference (this will then allow the blocks to be garbage-collected)
-
@@ -0,0 +1,101 @@
+++
+title = "Multi-HDD support"
+weight = 15
+++
+
+
+Since v0.9, Garage natively supports nodes that have several storage drives
+for storing data blocks (not for metadata storage).
+
+## Initial setup
+
+To set up a new Garage storage node with multiple HDDs,
+format and mount all your drives in different directories,
+and use a Garage configuration as follows:
+
+```toml
+data_dir = [
+    { path = "/path/to/hdd1", capacity = "2T" },
+    { path = "/path/to/hdd2", capacity = "4T" },
+]
+```
+
+Garage will automatically balance all blocks stored by the node
+among the different specified directories, proportionnally to the
+specified capacities.
+
+## Updating the list of storage locations
+
+If you add new storage locations to your `data_dir`,
+Garage will not rebalance existing data between storage locations.
+Newly written blocks will be balanced proportionnally to the specified capacities,
+and existing data may be moved between drives to improve balancing,
+but only opportunistically when a data block is re-written (e.g. an object
+is re-uploaded, or an object with a duplicate block is uploaded).
+
+To understand precisely what is happening, we need to dive in to how Garage
+splits data among the different storage locations.
+
+First of all, Garage divides the set of all possible block hashes
+in a fixed number of slices (currently 1024), and assigns
+to each slice a primary storage location among the specified data directories.
+The number of slices having their primary location in each data directory
+is proportionnal to the capacity specified in the config file.
+
+When Garage receives a block to write, it will always write it in the primary
+directory of the slice that contains its hash.
+
+Now, to be able to not lose existing data blocks when storage locations
+are added, Garage also keeps a list of secondary data directories
+for all of the hash slices. Secondary data directories for a slice indicates
+storage locations that once were primary directories for that slice, i.e. where
+Garage knows that data blocks of that slice might be stored.
+When Garage is requested to read a certain data block,
+it will first look in the primary storage directory of its slice,
+and if it doesn't find it there it goes through all of the secondary storage
+locations until it finds it. This allows Garage to continue operating
+normally when storage locations are added, without having to shuffle
+files between drives to place them in the correct location.
+
+This relatively simple strategy works well but does not ensure that data
+is correctly balanced among drives according to their capacity.
+To rebalance data, two strategies can be used:
+
+- Lazy rebalancing: when a block is re-written (e.g. the object is re-uploaded),
+  Garage checks whether the existing copy is in the primary directory of the slice
+  or in a secondary directory. If the current copy is in a secondary directory,
+  Garage re-writes a copy in the primary directory and deletes the one from the
+  secondary directory. This might never end up rebalancing everything if there
+  are data blocks that are only read and never written.
+
+- Active rebalancing: an operator of a Garage node can explicitly launch a repair
+  procedure that rebalances the data directories, moving all blocks to their
+  primary location. Once done, all secondary locations for all hash slices are
+  removed so that they won't be checked anymore when looking for a data block.
+
+## Read-only storage locations
+
+If you would like to move all data blocks from an existing data directory to one
+or several new data directories, mark the old directory as read-only:
+
+```toml
+data_dir = [
+    { path = "/path/to/old_data", read_only = true },
+    { path = "/path/to/new_hdd1", capacity = "2T" },
+    { path = "/path/to/new_hdd2", capacity = "4T" },
+]
+```
+
+Garage will be able to read requested blocks from the read-only directory.
+Garage will also move data out of the read-only directory either progressively
+(lazy rebalancing) or if requested explicitly (active rebalancing).
+
+Once an active rebalancing has finished, your read-only directory should be empty:
+it might still contain subdirectories, but no data files. You can check that
+it contains no files using:
+
+```bash
+find -type f /path/to/old_data      # should not print anything
+```
+
+at which point it can be removed from the `data_dir` list in your config file.
@@ -80,6 +80,6 @@ The entire procedure would look something like this:
 5. If any specific migration procedure is required, it is usually in one of the two cases:

  - It can be run on online nodes after the new version has started, during regular cluster operation.
-  - it has to be run offline
+  - it has to be run offline, in which case you will have to again take all nodes offline one after the other to run the repair

   For this last step, please refer to the specific documentation pertaining to the version upgrade you are doing.
@@ -209,7 +209,7 @@ one key can access multiple buckets, multiple keys can access one bucket.
 Create an API key using the following command:

 ```
-garage key new --name nextcloud-app-key
+garage key create nextcloud-app-key
 ```

 The output should look as follows:
@@ -269,14 +269,12 @@ named `~/.awsrc` with this content:
 export AWS_ACCESS_KEY_ID=xxxx      # put your Key ID here
 export AWS_SECRET_ACCESS_KEY=xxxx  # put your Secret key here
 export AWS_DEFAULT_REGION='garage'
-export AWS_ENDPOINT_URL='http://localhost:3900'
+export AWS_ENDPOINT='http://localhost:3900'

+function aws { command aws --endpoint-url $AWS_ENDPOINT $@ ; }
 aws --version
 ```

-Note you need to have at least `awscli` `>=1.29.0` or `>=2.13.0`, otherwise you
-need to specify `--endpoint-url` explicitly on each `awscli` invocation.
-
 Now, each time you want to use `awscli` on this target, run:

 ```bash
@@ -10,6 +10,8 @@ Here is an example `garage.toml` configuration file that illustrates all of the
 ```toml
 metadata_dir = "/var/lib/garage/meta"
 data_dir = "/var/lib/garage/data"
+metadata_fsync = true
+data_fsync = false

 db_engine = "lmdb"

@@ -90,6 +92,19 @@ This folder can be placed on an HDD. The space available for `data_dir`
 should be counted to determine a node's capacity
 when [adding it to the cluster layout](@/documentation/cookbook/real-world.md).

+Since `v0.9.0`, Garage supports multiple data directories with the following syntax:
+
+```toml
+data_dir = [
+    { path = "/path/to/old_data", read_only = true },
+    { path = "/path/to/new_hdd1", capacity = "2T" },
+    { path = "/path/to/new_hdd2", capacity = "4T" },
+]
+```
+
+See [the dedicated documentation page](@/documentation/operations/multi-hdd.md)
+on how to operate Garage in such a setup.
+
 ### `db_engine` (since `v0.8.0`)

 By default, Garage uses the Sled embedded database library
@@ -131,6 +146,49 @@ convert-db -a <input db engine> -i <input db path> \
 Make sure to specify the full database path as presented in the table above,
 and not just the path to the metadata directory.

+### `metadata_fsync`
+
+Whether to enable synchronous mode for the database engine or not.
+This is disabled (`false`) by default.
+
+This reduces the risk of metadata corruption in case of power failures,
+at the cost of a significant drop in write performance,
+as Garage will have to pause to sync data to disk much more often
+(several times for API calls such as PutObject).
+
+Using this option reduces the risk of simultaneous metadata corruption on several
+cluster nodes, which could lead to data loss.
+
+If multi-site replication is used, this option is most likely not necessary, as
+it is extremely unlikely that two nodes in different locations will have a 
+power failure at the exact same time.
+
+(Metadata corruption on a single node is not an issue, the corrupted data file
+can always be deleted and reconstructed from the other nodes in the cluster.)
+
+Here is how this option impacts the different database engines:
+
+| Database | `metadata_fsync = false` (default) | `metadata_fsync = true`       |
+|----------|------------------------------------|-------------------------------|
+| Sled     | default options                    | *unsupported*                 |
+| Sqlite   | `PRAGMA synchronous = OFF`         | `PRAGMA synchronous = NORMAL` |
+| LMDB     | `MDB_NOMETASYNC` + `MDB_NOSYNC`    | `MDB_NOMETASYNC`              |
+
+Note that the Sqlite database is always ran in `WAL` mode (`PRAGMA journal_mode = WAL`).
+
+### `data_fsync`
+
+Whether to `fsync` data blocks and their containing directory after they are
+saved to disk.
+This is disabled (`false`) by default.
+
+This might reduce the risk that a data block is lost in rare
+situations such as simultaneous node losing power,
+at the cost of a moderate drop in write performance.
+
+Similarly to `metatada_fsync`, this is likely not necessary
+if geographical replication is used.
+
 ### `block_size`

 Garage splits stored objects in consecutive chunks of size `block_size`
@@ -276,7 +334,7 @@ Compression is done synchronously, setting a value too high will add latency to
 This value can be different between nodes, compression is done by the node which receive the
 API call.

-### `rpc_secret`, `rpc_secret_file` or `GARAGE_RPC_SECRET`, `GARAGE_RPC_SECRET_FILE` (env)
+### `rpc_secret`, `rpc_secret_file` or `GARAGE_RPC_SECRET` (env)

 Garage uses a secret key, called an RPC secret, that is shared between all
 nodes of the cluster in order to identify these nodes and allow them to
@@ -288,9 +346,6 @@ Since Garage `v0.8.2`, the RPC secret can also be stored in a file whose path is
 given in the configuration variable `rpc_secret_file`, or specified as an
 environment variable `GARAGE_RPC_SECRET`.

-Since Garage `v0.9.0`, you can also specify the path of a file storing the secret
-as the `GARAGE_RPC_SECRET_FILE` environment variable.
-
 ### `rpc_bind_addr`

 The address and port on which to bind for inter-cluster communcations
@@ -323,17 +378,6 @@ be obtained by running `garage node id` and then included directly in the
 key will be returned by `garage node id` and you will have to add the IP
 yourself.

-### `allow_world_readable_secrets`
-
-Garage checks the permissions of your secret files to make sure they're not
-world-readable. In some cases, the check might fail and consider your files as
-world-readable even if they're not, for instance when using Posix ACLs.
-
-Setting `allow_world_readable_secrets` to `true` bypass this
-permission verification.
-
-Alternatively, you can set the `GARAGE_ALLOW_WORLD_READABLE_SECRETS`
-environment variable to `true` to bypass the permissions check.

 ## The `[consul_discovery]` section

@@ -424,8 +468,6 @@ manually.
 The IP and port on which to bind for accepting S3 API calls.
 This endpoint does not suport TLS: a reverse proxy should be used to provide it.

-Alternatively, since `v0.8.5`, a path can be used to create a unix socket with 0222 mode.
-
 ### `s3_region`

 Garage will accept S3 API calls that are targetted to the S3 region defined here.
@@ -455,8 +497,6 @@ The IP and port on which to bind for accepting HTTP requests to buckets configur
 for website access.
 This endpoint does not suport TLS: a reverse proxy should be used to provide it.

-Alternatively, since `v0.8.5`, a path can be used to create a unix socket with 0222 mode.
-
 ### `root_domain`

 The optional suffix appended to bucket names for the corresponding HTTP Host.
@@ -476,10 +516,7 @@ If specified, Garage will bind an HTTP server to this port and address, on
 which it will listen to requests for administration features.
 See [administration API reference](@/documentation/reference-manual/admin-api.md) to learn more about these features.

-Alternatively, since `v0.8.5`, a path can be used to create a unix socket. Note that for security reasons,
-the socket will have 0220 mode. Make sure to set user and group permissions accordingly.
-
-### `metrics_token`, `metrics_token_file` or `GARAGE_METRICS_TOKEN`, `GARAGE_METRICS_TOKEN_FILE` (env)
+### `metrics_token`, `metrics_token_file` or `GARAGE_METRICS_TOKEN` (env)

 The token for accessing the Metrics endpoint. If this token is not set, the
 Metrics endpoint can be accessed without access control.
@@ -489,9 +526,8 @@ You can use any random string for this value. We recommend generating a random t
 `metrics_token` was introduced in Garage `v0.7.2`.
 `metrics_token_file` and the `GARAGE_METRICS_TOKEN` environment variable are supported since Garage `v0.8.2`.

-`GARAGE_METRICS_TOKEN_FILE` is supported since `v0.9.0`.

-### `admin_token`, `admin_token_file` or `GARAGE_ADMIN_TOKEN`, `GARAGE_ADMIN_TOKEN_FILE` (env)
+### `admin_token`, `admin_token_file` or `GARAGE_ADMIN_TOKEN` (env)

 The token for accessing all of the other administration endpoints.  If this
 token is not set, access to these endpoints is disabled entirely.
@@ -501,7 +537,6 @@ You can use any random string for this value. We recommend generating a random t
 `admin_token` was introduced in Garage `v0.7.2`.
 `admin_token_file` and the `GARAGE_ADMIN_TOKEN` environment variable are supported since Garage `v0.8.2`.

-`GARAGE_ADMIN_TOKEN_FILE` is supported since `v0.9.0`.

 ### `trace_sink`

@@ -75,16 +75,13 @@ but these endpoints are documented in [Red Hat Ceph Storage - Chapter 2. Ceph Ob

 | Endpoint                     | Garage                           | [Openstack Swift](https://docs.openstack.org/swift/latest/s3_compat.html) | [Ceph Object Gateway](https://docs.ceph.com/en/latest/radosgw/s3/) | [Riak CS](https://docs.riak.com/riak/cs/2.1.1/references/apis/storage/s3/index.html) | [OpenIO](https://docs.openio.io/latest/source/arch-design/s3_compliancy.html) |
 |------------------------------|----------------------------------|-----------------|---------------|---------|-----|
-| [AbortMultipartUpload](https://docs.aws.amazon.com/AmazonS3/latest/API/API_AbortMultipartUpload.html)         | ✅ Implemented                      |  ✅ | ✅ | ✅ | ✅ |
-| [CompleteMultipartUpload](https://docs.aws.amazon.com/AmazonS3/latest/API/API_CompleteMultipartUpload.html)   | ✅ Implemented (see details below)                      | ✅ | ✅ | ✅ | ✅ |
-| [CreateMultipartUpload](https://docs.aws.amazon.com/AmazonS3/latest/API/API_CreateMultipartUpload.html)        | ✅ Implemented                      | ✅| ✅ | ✅ | ✅ |
-| [ListMultipartUpload](https://docs.aws.amazon.com/AmazonS3/latest/API/API_ListMultipartUpload.html)          | ✅ Implemented                      | ✅ | ✅ | ✅ | ✅ |
-| [ListParts](https://docs.aws.amazon.com/AmazonS3/latest/API/API_ListParts.html)                    | ✅ Implemented                      | ✅ | ✅ | ✅ | ✅ |
-| [UploadPart](https://docs.aws.amazon.com/AmazonS3/latest/API/API_UploadPart.html)                  | ✅ Implemented (see details below)                      | ✅ | ✅| ✅ | ✅ |
-| [UploadPartCopy](https://docs.aws.amazon.com/AmazonS3/latest/API/API_UploadPartCopy.html)               | ✅ Implemented                      | ✅ | ✅ | ✅ | ✅ |
-
-Our implementation of Multipart Upload is currently a bit more restrictive than Amazon's one in some edge cases.
-For more information, please refer to our [issue tracker](https://git.deuxfleurs.fr/Deuxfleurs/garage/issues/204).
+| [AbortMultipartUpload](https://docs.aws.amazon.com/AmazonS3/latest/API/API_AbortMultipartUpload.html)         | ✅ Implemented  |  ✅ | ✅ | ✅ | ✅ |
+| [CompleteMultipartUpload](https://docs.aws.amazon.com/AmazonS3/latest/API/API_CompleteMultipartUpload.html)   | ✅ Implemented  | ✅ | ✅ | ✅ | ✅ |
+| [CreateMultipartUpload](https://docs.aws.amazon.com/AmazonS3/latest/API/API_CreateMultipartUpload.html)        | ✅ Implemented | ✅| ✅ | ✅ | ✅ |
+| [ListMultipartUpload](https://docs.aws.amazon.com/AmazonS3/latest/API/API_ListMultipartUpload.html)          | ✅ Implemented   | ✅ | ✅ | ✅ | ✅ |
+| [ListParts](https://docs.aws.amazon.com/AmazonS3/latest/API/API_ListParts.html)                    | ✅ Implemented             | ✅ | ✅ | ✅ | ✅ |
+| [UploadPart](https://docs.aws.amazon.com/AmazonS3/latest/API/API_UploadPart.html)                  | ✅ Implemented             | ✅ | ✅| ✅ | ✅ |
+| [UploadPartCopy](https://docs.aws.amazon.com/AmazonS3/latest/API/API_UploadPartCopy.html)               | ✅ Implemented        | ✅ | ✅ | ✅ | ✅ |

 ### Website endpoints

@@ -127,15 +124,22 @@ If you need this feature, please [share your use case in our dedicated issue](ht

 | Endpoint                     | Garage                           | [Openstack Swift](https://docs.openstack.org/swift/latest/s3_compat.html) | [Ceph Object Gateway](https://docs.ceph.com/en/latest/radosgw/s3/) | [Riak CS](https://docs.riak.com/riak/cs/2.1.1/references/apis/storage/s3/index.html) | [OpenIO](https://docs.openio.io/latest/source/arch-design/s3_compliancy.html) |
 |------------------------------|----------------------------------|-----------------|---------------|---------|-----|
-| [DeleteBucketLifecycle](https://docs.aws.amazon.com/AmazonS3/latest/API/API_DeleteBucketLifecycle.html) | ❌ Missing | ❌| ✅| ❌| ✅|
-| [GetBucketLifecycleConfiguration](https://docs.aws.amazon.com/AmazonS3/latest/API/API_GetBucketLifecycleConfiguration.html) | ❌ Missing | ❌| ✅ | ❌| ✅|
-| [PutBucketLifecycleConfiguration](https://docs.aws.amazon.com/AmazonS3/latest/API/API_PutBucketLifecycleConfiguration.html) | ❌ Missing | ❌| ✅ | ❌| ✅|
+| [DeleteBucketLifecycle](https://docs.aws.amazon.com/AmazonS3/latest/API/API_DeleteBucketLifecycle.html) | ✅ Implemented | ❌| ✅| ❌| ✅|
+| [GetBucketLifecycleConfiguration](https://docs.aws.amazon.com/AmazonS3/latest/API/API_GetBucketLifecycleConfiguration.html) | ✅ Implemented | ❌| ✅ | ❌| ✅|
+| [PutBucketLifecycleConfiguration](https://docs.aws.amazon.com/AmazonS3/latest/API/API_PutBucketLifecycleConfiguration.html) | ⚠ Partially implemented (see below) | ❌| ✅ | ❌| ✅|
 | [GetBucketVersioning](https://docs.aws.amazon.com/AmazonS3/latest/API/API_GetBucketVersioning.html)          | ❌ Stub (see below)       | ✅| ✅ | ❌| ✅|
 | [ListObjectVersions](https://docs.aws.amazon.com/AmazonS3/latest/API/API_ListObjectVersions.html) | ❌ Missing | ❌| ✅ | ❌| ✅|
 | [PutBucketVersioning](https://docs.aws.amazon.com/AmazonS3/latest/API/API_PutBucketVersioning.html) | ❌ Missing | ❌| ✅| ❌| ✅|

+**PutBucketLifecycleConfiguration:** The only actions supported are
+`AbortIncompleteMultipartUpload` and `Expiration` (without the
+`ExpiredObjectDeleteMarker` field).  All other operations are dependent on
+either bucket versionning or storage classes which Garage currently does not
+implement. The deprecated `Prefix` member directly in the the `Rule`
+structure/XML tag is not supported, specified prefixes must be inside the
+`Filter` structure/XML tag.

-**GetBucketVersioning:** Stub implementation (Garage does not yet support versionning so this always returns "versionning not enabled").
+**GetBucketVersioning:** Stub implementation which always returns "versionning not enabled", since Garage does not yet support bucket versionning.

 ### Replication endpoints

@@ -52,11 +52,11 @@ Returns an HTTP status 200 if the node is ready to answer user's requests,
 and an HTTP status 503 (Service Unavailable) if there are some partitions
 for which a quorum of nodes is not available.
 A simple textual message is also returned in a body with content-type `text/plain`.
-See `/v0/health` for an API that also returns JSON output.
+See `/v1/health` for an API that also returns JSON output.

 ### Cluster operations

-#### GetClusterStatus `GET /v0/status`
+#### GetClusterStatus `GET /v1/status`

 Returns the cluster's current status in JSON, including:

@@ -70,86 +70,112 @@ Example response body:
 ```json
 {
  "node": "ec79480e0ce52ae26fd00c9da684e4fa56658d9c64cdcecb094e936de0bfe71f",
-  "garage_version": "git:v0.8.0",
-  "knownNodes": {
-    "ec79480e0ce52ae26fd00c9da684e4fa56658d9c64cdcecb094e936de0bfe71f": {
+  "garageVersion": "git:v0.9.0-dev",
+  "garageFeatures": [
+    "k2v",
+    "sled",
+    "lmdb",
+    "sqlite",
+    "metrics",
+    "bundled-libs"
+  ],
+  "rustVersion": "1.68.0",
+  "dbEngine": "LMDB (using Heed crate)",
+  "knownNodes": [
+    {
+      "id": "ec79480e0ce52ae26fd00c9da684e4fa56658d9c64cdcecb094e936de0bfe71f",
      "addr": "10.0.0.11:3901",
-      "is_up": true,
-      "last_seen_secs_ago": 9,
+      "isUp": true,
+      "lastSeenSecsAgo": 9,
      "hostname": "node1"
    },
-    "4a6ae5a1d0d33bf895f5bb4f0a418b7dc94c47c0dd2eb108d1158f3c8f60b0ff": {
+    {
+      "id": "4a6ae5a1d0d33bf895f5bb4f0a418b7dc94c47c0dd2eb108d1158f3c8f60b0ff",
      "addr": "10.0.0.12:3901",
-      "is_up": true,
-      "last_seen_secs_ago": 1,
+      "isUp": true,
+      "lastSeenSecsAgo": 1,
      "hostname": "node2"
    },
-    "23ffd0cdd375ebff573b20cc5cef38996b51c1a7d6dbcf2c6e619876e507cf27": {
+    {
+      "id": "23ffd0cdd375ebff573b20cc5cef38996b51c1a7d6dbcf2c6e619876e507cf27",
      "addr": "10.0.0.21:3901",
-      "is_up": true,
-      "last_seen_secs_ago": 7,
+      "isUp": true,
+      "lastSeenSecsAgo": 7,
      "hostname": "node3"
    },
-    "e2ee7984ee65b260682086ec70026165903c86e601a4a5a501c1900afe28d84b": {
+    {
+      "id": "e2ee7984ee65b260682086ec70026165903c86e601a4a5a501c1900afe28d84b",
      "addr": "10.0.0.22:3901",
-      "is_up": true,
-      "last_seen_secs_ago": 1,
+      "isUp": true,
+      "lastSeenSecsAgo": 1,
      "hostname": "node4"
    }
-  },
+  ],
  "layout": {
    "version": 12,
-    "roles": {
-      "ec79480e0ce52ae26fd00c9da684e4fa56658d9c64cdcecb094e936de0bfe71f": {
+    "roles": [
+      {
+        "id": "ec79480e0ce52ae26fd00c9da684e4fa56658d9c64cdcecb094e936de0bfe71f",
        "zone": "dc1",
-        "capacity": 4,
+        "capacity": 10737418240,
        "tags": [
          "node1"
        ]
      },
-      "4a6ae5a1d0d33bf895f5bb4f0a418b7dc94c47c0dd2eb108d1158f3c8f60b0ff": {
+      {
+        "id": "4a6ae5a1d0d33bf895f5bb4f0a418b7dc94c47c0dd2eb108d1158f3c8f60b0ff",
        "zone": "dc1",
-        "capacity": 6,
+        "capacity": 10737418240,
        "tags": [
          "node2"
        ]
      },
-      "23ffd0cdd375ebff573b20cc5cef38996b51c1a7d6dbcf2c6e619876e507cf27": {
+      {
+        "id": "23ffd0cdd375ebff573b20cc5cef38996b51c1a7d6dbcf2c6e619876e507cf27",
        "zone": "dc2",
-        "capacity": 10,
+        "capacity": 10737418240,
        "tags": [
          "node3"
        ]
      }
-    },
-    "stagedRoleChanges": {
-      "e2ee7984ee65b260682086ec70026165903c86e601a4a5a501c1900afe28d84b": {
+    ],
+    "stagedRoleChanges": [
+      {
+        "id": "e2ee7984ee65b260682086ec70026165903c86e601a4a5a501c1900afe28d84b",
+        "remove": false,
        "zone": "dc2",
-        "capacity": 5,
+        "capacity": 10737418240,
        "tags": [
          "node4"
        ]
      }
-    }
+      {
+        "id": "23ffd0cdd375ebff573b20cc5cef38996b51c1a7d6dbcf2c6e619876e507cf27",
+        "remove": true,
+        "zone": null,
+        "capacity": null,
+        "tags": null,
+      }
+    ]
  }
 }
 ```

-#### GetClusterHealth `GET /v0/health`
+#### GetClusterHealth `GET /v1/health`

 Returns the cluster's current health in JSON format, with the following variables:

- `status`: one of `Healthy`, `Degraded` or `Unavailable`:
-  - Healthy: Garage node is connected to all storage nodes
-  - Degraded: Garage node is not connected to all storage nodes, but a quorum of write nodes is available for all partitions
-  - Unavailable: a quorum of write nodes is not available for some partitions
- `known_nodes`: the number of nodes this Garage node has had a TCP connection to since the daemon started
- `connected_nodes`: the nubmer of nodes this Garage node currently has an open connection to
- `storage_nodes`: the number of storage nodes currently registered in the cluster layout
- `storage_nodes_ok`: the number of storage nodes to which a connection is currently open
+- `status`: one of `healthy`, `degraded` or `unavailable`:
+  - healthy: Garage node is connected to all storage nodes
+  - degraded: Garage node is not connected to all storage nodes, but a quorum of write nodes is available for all partitions
+  - unavailable: a quorum of write nodes is not available for some partitions
+- `knownNodes`: the number of nodes this Garage node has had a TCP connection to since the daemon started
+- `connectedNodes`: the nubmer of nodes this Garage node currently has an open connection to
+- `storageNodes`: the number of storage nodes currently registered in the cluster layout
+- `storageNodesOk`: the number of storage nodes to which a connection is currently open
 - `partitions`: the total number of partitions of the data (currently always 256)
- `partitions_quorum`: the number of partitions for which a quorum of write nodes is available
- `partitions_all_ok`: the number of partitions for which we are connected to all storage nodes responsible of storing it
+- `partitionsQuorum`: the number of partitions for which a quorum of write nodes is available
+- `partitionsAllOk`: the number of partitions for which we are connected to all storage nodes responsible of storing it

 Contrarily to `GET /health`, this endpoint always returns a 200 OK HTTP response code.

@@ -157,18 +183,18 @@ Example response body:

 ```json
 {
-    "status": "Degraded",
-    "known_nodes": 3,
-    "connected_nodes": 2,
-    "storage_nodes": 3,
-    "storage_nodes_ok": 2,
-    "partitions": 256,
-    "partitions_quorum": 256,
-    "partitions_all_ok": 0
+  "status": "degraded",
+  "knownNodes": 3,
+  "connectedNodes": 3,
+  "storageNodes": 4,
+  "storageNodesOk": 3,
+  "partitions": 256,
+  "partitionsQuorum": 256,
+  "partitionsAllOk": 64
 }
 ```

-#### ConnectClusterNodes `POST /v0/connect`
+#### ConnectClusterNodes `POST /v1/connect`

 Instructs this Garage node to connect to other Garage nodes at specified addresses.

@@ -198,7 +224,7 @@ Example response:
 ]
 ```

-#### GetClusterLayout `GET /v0/layout`
+#### GetClusterLayout `GET /v1/layout`

 Returns the cluster's current layout in JSON, including:

@@ -212,42 +238,54 @@ Example response body:
 ```json
 {
  "version": 12,
-  "roles": {
-    "ec79480e0ce52ae26fd00c9da684e4fa56658d9c64cdcecb094e936de0bfe71f": {
+  "roles": [
+    {
+      "id": "ec79480e0ce52ae26fd00c9da684e4fa56658d9c64cdcecb094e936de0bfe71f",
      "zone": "dc1",
-      "capacity": 4,
+      "capacity": 10737418240,
      "tags": [
        "node1"
      ]
    },
-    "4a6ae5a1d0d33bf895f5bb4f0a418b7dc94c47c0dd2eb108d1158f3c8f60b0ff": {
+    {
+      "id": "4a6ae5a1d0d33bf895f5bb4f0a418b7dc94c47c0dd2eb108d1158f3c8f60b0ff",
      "zone": "dc1",
-      "capacity": 6,
+      "capacity": 10737418240,
      "tags": [
        "node2"
      ]
    },
-    "23ffd0cdd375ebff573b20cc5cef38996b51c1a7d6dbcf2c6e619876e507cf27": {
+    {
+      "id": "23ffd0cdd375ebff573b20cc5cef38996b51c1a7d6dbcf2c6e619876e507cf27",
      "zone": "dc2",
-      "capacity": 10,
+      "capacity": 10737418240,
      "tags": [
        "node3"
      ]
    }
-  },
-  "stagedRoleChanges": {
-    "e2ee7984ee65b260682086ec70026165903c86e601a4a5a501c1900afe28d84b": {
+  ],
+  "stagedRoleChanges": [
+    {
+      "id": "e2ee7984ee65b260682086ec70026165903c86e601a4a5a501c1900afe28d84b",
+      "remove": false,
      "zone": "dc2",
-      "capacity": 5,
+      "capacity": 10737418240,
      "tags": [
        "node4"
      ]
    }
-  }
+    {
+      "id": "23ffd0cdd375ebff573b20cc5cef38996b51c1a7d6dbcf2c6e619876e507cf27",
+      "remove": true,
+      "zone": null,
+      "capacity": null,
+      "tags": null,
+    }
+  ]
 }
 ```

-#### UpdateClusterLayout `POST /v0/layout`
+#### UpdateClusterLayout `POST /v1/layout`

 Send modifications to the cluster layout. These modifications will
 be included in the staged role changes, visible in subsequent calls
@@ -259,8 +297,9 @@ the layout.
 Request body format:

 ```json
-{
-  <node_id>: {
+[
+  {
+    "id": <node_id>,
    "capacity": <new_capacity>,
    "zone": <new_zone>,
    "tags": [
@@ -268,17 +307,22 @@ Request body format:
      ...
    ]
  },
-  <node_id_to_remove>: null,
-  ...
-}
+  {
+    "id": <node_id_to_remove>,
+    "remove": true
+  }
+]
 ```

 Contrary to the CLI that may update only a subset of the fields
 `capacity`, `zone` and `tags`, when calling this API all of these
 values must be specified.

+This returns the new cluster layout with the proposed staged changes,
+as returned by GetClusterLayout.

-#### ApplyClusterLayout `POST /v0/layout/apply`
+
+#### ApplyClusterLayout `POST /v1/layout/apply`

 Applies to the cluster the layout changes currently registered as
 staged layout changes.
@@ -295,7 +339,10 @@ Similarly to the CLI, the body must include the version of the new layout
 that will be created, which MUST be 1 + the value of the currently
 existing layout in the cluster.

-#### RevertClusterLayout `POST /v0/layout/revert`
+This returns the message describing all the calculations done to compute the new
+layout, as well as the description of the layout as returned by GetClusterLayout.
+
+#### RevertClusterLayout `POST /v1/layout/revert`

 Clears all of the staged layout changes.

@@ -313,10 +360,13 @@ Similarly to the CLI, the body must include the incremented
 version number, which MUST be 1 + the value of the currently
 existing layout in the cluster.

+This returns the new cluster layout with all changes reverted,
+as returned by GetClusterLayout.
+

 ### Access key operations

-#### ListKeys `GET /v0/key`
+#### ListKeys `GET /v1/key`

 Returns all API access keys in the cluster.

@@ -335,34 +385,8 @@ Example response:
 ]
 ```

-#### CreateKey `POST /v0/key`
-
-Creates a new API access key.
-
-Request body format:
-
-```json
-{
-    "name": "NameOfMyKey"
-}
-```
-
-#### ImportKey `POST /v0/key/import`
-
-Imports an existing API key.
-
-Request body format:
-
-```json
-{
-    "accessKeyId": "GK31c2f218a2e44f485b94239e",
-    "secretAccessKey": "b892c0665f0ada8a4755dae98baa3b133590e11dae3bcc1f9d769d67f16c3835",
-    "name": "NameOfMyKey"
-}
-```
-
-#### GetKeyInfo `GET /v0/key?id=<acces key id>`
-#### GetKeyInfo `GET /v0/key?search=<pattern>`
+#### GetKeyInfo `GET /v1/key?id=<acces key id>`
+#### GetKeyInfo `GET /v1/key?search=<pattern>`

 Returns information about the requested API access key.

@@ -370,6 +394,9 @@ If `id` is set, the key is looked up using its exact identifier (faster).
 If `search` is set, the key is looked up using its name or prefix
 of identifier (slower, all keys are enumerated to do this).

+Optionnally, the query parameter `showSecretKey=true` can be set to reveal the
+associated secret access key.
+
 Example response:

 ```json
@@ -433,11 +460,40 @@ Example response:
 }
 ```

-#### DeleteKey `DELETE /v0/key?id=<acces key id>`
+#### CreateKey `POST /v1/key`

-Deletes an API access key.
+Creates a new API access key.

-#### UpdateKey `POST /v0/key?id=<acces key id>`
+Request body format:
+
+```json
+{
+    "name": "NameOfMyKey"
+}
+```
+
+This returns the key info, including the created secret key,
+in the same format as the result of GetKeyInfo.
+
+#### ImportKey `POST /v1/key/import`
+
+Imports an existing API key.
+This will check that the imported key is in the valid format, i.e.
+is a key that could have been generated by Garage.
+
+Request body format:
+
+```json
+{
+    "accessKeyId": "GK31c2f218a2e44f485b94239e",
+    "secretAccessKey": "b892c0665f0ada8a4755dae98baa3b133590e11dae3bcc1f9d769d67f16c3835",
+    "name": "NameOfMyKey"
+}
+```
+
+This returns the key info in the same format as the result of GetKeyInfo.
+
+#### UpdateKey `POST /v1/key?id=<acces key id>`

 Updates information about the specified API access key.

@@ -457,10 +513,16 @@ All fields (`name`, `allow` and `deny`) are optional.
 If they are present, the corresponding modifications are applied to the key, otherwise nothing is changed.
 The possible flags in `allow` and `deny` are: `createBucket`.

+This returns the key info in the same format as the result of GetKeyInfo.
+
+#### DeleteKey `DELETE /v1/key?id=<acces key id>`
+
+Deletes an API access key.
+

 ### Bucket operations

-#### ListBuckets `GET /v0/bucket`
+#### ListBuckets `GET /v1/bucket`

 Returns all storage buckets in the cluster.

@@ -502,8 +564,8 @@ Example response:
 ]
 ```

-#### GetBucketInfo `GET /v0/bucket?id=<bucket id>`
-#### GetBucketInfo `GET /v0/bucket?globalAlias=<alias>`
+#### GetBucketInfo `GET /v1/bucket?id=<bucket id>`
+#### GetBucketInfo `GET /v1/bucket?globalAlias=<alias>`

 Returns information about the requested storage bucket.

@@ -535,7 +597,10 @@ Example response:
        ],
        "objects": 14827,
        "bytes": 13189855625,
-        "unfinshedUploads": 0,
+        "unfinishedUploads": 1,
+        "unfinishedMultipartUploads": 1,
+        "unfinishedMultipartUploadParts": 11,
+        "unfinishedMultipartUploadBytes": 41943040,
        "quotas": {
            "maxSize": null,
            "maxObjects": null
@@ -543,7 +608,7 @@ Example response:
 }
 ```

-#### CreateBucket `POST /v0/bucket`
+#### CreateBucket `POST /v1/bucket`

 Creates a new storage bucket.

@@ -583,13 +648,7 @@ or no alias at all.
 Technically, you can also specify both `globalAlias` and `localAlias` and that would create
 two aliases, but I don't see why you would want to do that.

-#### DeleteBucket `DELETE /v0/bucket?id=<bucket id>`
-
-Deletes a storage bucket. A bucket cannot be deleted if it is not empty.
-
-Warning: this will delete all aliases associated with the bucket!
-
-#### UpdateBucket `PUT /v0/bucket?id=<bucket id>`
+#### UpdateBucket `PUT /v1/bucket?id=<bucket id>`

 Updates configuration of the given bucket.

@@ -621,9 +680,16 @@ In `quotas`: new values of `maxSize` and `maxObjects` must both be specified, or
 to remove the quotas. An absent value will be considered the same as a `null`. It is not possible
 to change only one of the two quotas.

+#### DeleteBucket `DELETE /v1/bucket?id=<bucket id>`
+
+Deletes a storage bucket. A bucket cannot be deleted if it is not empty.
+
+Warning: this will delete all aliases associated with the bucket!
+
+
 ### Operations on permissions for keys on buckets

-#### BucketAllowKey `POST /v0/bucket/allow`
+#### BucketAllowKey `POST /v1/bucket/allow`

 Allows a key to do read/write/owner operations on a bucket.

@@ -644,7 +710,7 @@ Request body format:
 Flags in `permissions` which have the value `true` will be activated.
 Other flags will remain unchanged.

-#### BucketDenyKey `POST /v0/bucket/deny`
+#### BucketDenyKey `POST /v1/bucket/deny`

 Denies a key from doing read/write/owner operations on a bucket.

@@ -668,19 +734,19 @@ Other flags will remain unchanged.

 ### Operations on bucket aliases

-#### GlobalAliasBucket `PUT /v0/bucket/alias/global?id=<bucket id>&alias=<global alias>`
+#### GlobalAliasBucket `PUT /v1/bucket/alias/global?id=<bucket id>&alias=<global alias>`

 Empty body. Creates a global alias for a bucket.

-#### GlobalUnaliasBucket `DELETE /v0/bucket/alias/global?id=<bucket id>&alias=<global alias>`
+#### GlobalUnaliasBucket `DELETE /v1/bucket/alias/global?id=<bucket id>&alias=<global alias>`

 Removes a global alias for a bucket.

-#### LocalAliasBucket `PUT /v0/bucket/alias/local?id=<bucket id>&accessKeyId=<access key ID>&alias=<local alias>`
+#### LocalAliasBucket `PUT /v1/bucket/alias/local?id=<bucket id>&accessKeyId=<access key ID>&alias=<local alias>`

 Empty body. Creates a local alias for a bucket in the namespace of a specific access key.

-#### LocalUnaliasBucket `DELETE /v0/bucket/alias/local?id=<bucket id>&accessKeyId<access key ID>&alias=<local alias>`
+#### LocalUnaliasBucket `DELETE /v1/bucket/alias/local?id=<bucket id>&accessKeyId<access key ID>&alias=<local alias>`

 Removes a local alias for a bucket in the namespace of a specific access key.

@@ -0,0 +1,13 @@
+optimal_layout.aux
+optimal_layout.log
+optimal_layout.synctex.gz
+optimal_layout.bbl
+optimal_layout.blg
+
+geodistrib.aux
+geodistrib.bbl
+geodistrib.blg
+geodistrib.log
+geodistrib.out
+geodistrib.synctex.gz
+
@@ -0,0 +1,317 @@
+\documentclass[]{article}
+
+\usepackage{amsmath,amssymb}
+\usepackage{amsthm}
+
+\usepackage{stmaryrd}
+
+\usepackage{graphicx,xcolor}
+\usepackage{hyperref}
+
+\usepackage{algorithm,algpseudocode,float} 
+
+\renewcommand\thesubsubsection{\Alph{subsubsection})}
+
+\newtheorem{proposition}{Proposition}
+
+%opening
+\title{An algorithm for geo-distributed and redundant storage in Garage}
+\author{Mendes Oulamara \\ \emph{mendes@deuxfleurs.fr}}
+\date{}
+
+\begin{document}
+
+\maketitle
+
+\begin{abstract}
+	Garage
+\end{abstract}
+
+\section{Introduction}
+
+Garage\footnote{\url{https://garagehq.deuxfleurs.fr/}} is an open-source distributed object storage service tailored for self-hosting. It was designed by the Deuxfleurs association\footnote{\url{https://deuxfleurs.fr/}} to enable small structures (associations, collectives, small companies) to share storage resources to reliably self-host their data, possibly with old and non-reliable machines.
+
+To achieve these reliability and availability goals, the data is broken into \emph{partitions} and every partition is replicated over 3 different machines (that we call \emph{nodes}). When the data is queried, a consensus algorithm allows to fetch it from one of the nodes. A \emph{replication factor} of 3 ensures the best guarantees in the consensus algorithm \cite{ADD RREF}, but this parameter can be different.
+
+Moreover, if the nodes are spread over different \emph{zones} (different houses, offices, cities\dots), we can ask the data to be replicated over nodes belonging to different zones, to improve the storage robustness against zone failure (such as power outage). To do so, we set a \emph{redundancy parameter}, that is no more than the replication factor, and we ask that any partition is replicated over this number of zones at least.
+
+In this work, we propose a repartition algorithm that, given the nodes specifications and the replication and redundancy parameters, computes an optimal assignation of partitions to nodes. We say that the assignation is optimal in the sense that it maximizes the size of the partitions, and hence the effective storage capacity of the system.
+
+Moreover, when a former assignation exists, which is not optimal anymore due to nodes or zones updates, our algorithm computes a new optimal assignation that minimizes the amount of data to be transferred during the assignation update (the \emph{transfer load}).
+
+We call the set of nodes cooperating to store the data a \emph{cluster}, and a description of the nodes, zones and the assignation of partitions to nodes a \emph{cluster layout}
+
+\subsection{Notations}
+
+Let $k$ be some fixed parameter value, typically 8, that we call the ``partition bits''.
+Every object to be stored in the system is split into data blocks of fixed size. We compute a hash $h(\mathbf{b})$ of every such block $\mathbf{b}$, and we define the $k$ last bits of this hash to be the partition number $p(\mathbf{b})$ of the block. This label can take $P=2^k$ different values, and hence there are $P$ different partitions. We denote $\mathbf{P}$ the set of partition labels (i.e. $\mathbf{P}=\llbracket1,P\rrbracket$).
+
+We are given a set $\mathbf{N}$ of $N$ nodes  and a set  $\mathbf{Z}$ of $Z$ zones. Every node $n$ has a non-negative storage capacity $c_n\ge 0$ and belongs to a zone $z_n\in \mathbf{Z}$. We are also given a replication parameter $\rho_\mathbf{N}$ and a redundancy parameter $\rho_\mathbf{Z}$ such that  $1\le \rho_\mathbf{Z} \le \rho_\mathbf{N}$ (typical values would be $\rho_N=3$ and $\rho_Z=2$).
+
+Our goal is to compute an assignment $\alpha = (\alpha_p^1, \ldots, \alpha_p^{\rho_\mathbf{N}})_{p\in \mathbf{P}}$ such that every partition $p$ is associated to $\rho_\mathbf{N}$ distinct nodes $\alpha_p^1, \ldots, \alpha_p^{\rho_\mathbf{N}} \in \mathbf{N}$ and these nodes belong to at least $\rho_\mathbf{Z}$ distinct zones. Among the possible assignations, we choose one that \emph{maximizes} the effective storage capacity of the cluster. If the layout contained a previous assignment $\alpha'$, we \emph{minimize} the amount of data to transfer during the layout update by making $\alpha$ as close as possible to $\alpha'$. These maximization and minimization are described more formally in the following section.
+
+\subsection{Optimization parameters}
+
+To link the effective storage capacity of the cluster to partition assignment, we make the following assumption:
+\begin{equation}
+	\tag{H1}
+	\text{\emph{All partitions have the same size $s$.}}
+\end{equation}
+This assumption is justified by the dispersion of the hashing function, when the number of partitions is small relative to the number of stored blocks.
+
+Every node $n$ wille store some number $p_n$ of partitions (it is the number of partitions $p$ such that $n$ appears in the $\alpha_p$). Hence the partitions stored by $n$ (and hence all partitions by our assumption) have there size bounded by $c_n/p_n$. This remark leads us to define the optimal size that we will want to maximize:
+
+\begin{equation}
+	\label{eq:optimal}
+	\tag{OPT}
+s^* = \min_{n \in N} \frac{c_n}{p_n}.
+\end{equation}
+
+When the capacities of the nodes are updated (this includes adding or removing a node), we want to update the assignment as well. However, transferring the data between nodes has a cost and we would like to limit the number of changes in the assignment. We make the following assumption:
+\begin{equation}
+	\tag{H2}
+	\text{\emph{Nodes updates happen rarely relatively to block operations.}}
+\end{equation}
+This assumption justifies that when we compute the new assignment $\alpha$, it is worth to optimize the partition size \eqref{eq:optimal} first, and then, among the possible optimal solution, to try to minimize the number of partition transfers. More formally, we minimize the distance between two assignments defined by
+\begin{equation}
+	d(\alpha, \alpha') := \#\{ (n,p) \in \mathbf{N}\times\mathbf{P} ~|~ n\in \alpha_p \triangle \alpha'_p \}
+\end{equation}
+where the symmetric difference $\alpha_p \triangle \alpha'_p$ denotes the nodes appearing in one of the assignations but not in both.
+
+\section{Computation of an optimal assignment}
+
+The algorithm that we propose takes as inputs the cluster layout parameters $\mathbf{N}$, $\mathbf{Z}$, $\mathbf{P}$, $(c_n)_{n\in \mathbf{N}}$, $\rho_\mathbf{N}$, $\rho_\mathbf{Z}$, that we defined in the introduction, together with the former assignation $\alpha'$ (if any). The computation of the new optimal assignation $\alpha^*$ is done in three successive steps that will be detailed in the following sections. The first step computes the largest partition size $s^*$ that an assignation can achieve. The second step computes an optimal candidate assignment $\alpha$ that achieves $s^*$ and a heuristic is used in the computation to make it hopefully close to $\alpha'$. The third steps modifies $\alpha$ iteratively to reduces $d(\alpha, \alpha')$ and yields an assignation $\alpha^*$ achieving $s^*$, and minimizing $d(\cdot, \alpha')$ among such assignations.
+
+We will explain in the next section how to represent an assignment $\alpha$ by a flow $f$ on a weighted graph $G$ to enable the use of flow and graph algorithms. The main function of the algorithm can be written as follows.
+
+\subsubsection*{Algorithm}
+
+\begin{algorithmic}[1]
+	\Function{Compute Layout}{$\mathbf{N}$, $\mathbf{Z}$, $\mathbf{P}$, $(c_n)_{n\in \mathbf{N}}$, $\rho_\mathbf{N}$, $\rho_\mathbf{Z}$, $\alpha'$}
+	\State $s^* \leftarrow$ \Call{Compute Partition Size}{$\mathbf{N}$, $\mathbf{Z}$, $\mathbf{P}$, $(c_n)_{n\in \mathbf{N}}$, $\rho_\mathbf{N}$, $\rho_\mathbf{Z}$}
+	\State $G \leftarrow G(s^*)$
+	\State $f \leftarrow$ 	\Call{Compute Candidate Assignment}{$G$, $\alpha'$}
+	\State $f^* \leftarrow$ 	\Call{Minimize transfer load}{$G$, $f$, $\alpha'$}
+	\State Build $\alpha^*$ from $f^*$
+	\State \Return $\alpha^*$
+	\EndFunction
+\end{algorithmic}
+
+\subsubsection*{Complexity}
+As we will see in the next sections, the worst case complexity of this algorithm is $O(P^2 N^2)$. The minimization of transfer load is the most expensive step, and it can run with a timeout since it is only an optimization step. Without this step (or with a smart timeout), the worst cas complexity can be $O((PN)^{3/2}\log C)$ where $C$ is the total storage capacity of the cluster. 
+
+\subsection{Determination of the partition size $s^*$}
+
+We will represent an assignment $\alpha$ as a flow in a specific graph $G$. We will not compute the optimal partition size $s^*$ a priori, but we will determine it by dichotomy, as the largest size $s$ such that the maximal flow achievable on $G=G(s)$ has value $\rho_\mathbf{N}P$. We will assume that the capacities are given in a small enough unit (say, Megabytes), and we will determine $s^*$ at the precision of the given unit.
+
+Given some candidate size value $s$, we describe the oriented weighted graph $G=(V,E)$ with vertex set $V$ arc set $E$ (see Figure \ref{fig:flowgraph}).
+
+The set of vertices $V$ contains the source $\mathbf{s}$, the sink $\mathbf{t}$, vertices 
+$\mathbf{p^+, p^-}$ for every partition $p$, vertices $\mathbf{x}_{p,z}$ for every partition $p$ and zone $z$, and vertices $\mathbf{n}$ for every node $n$. 
+
+The set of arcs $E$ contains:
+\begin{itemize}
+	\item ($\mathbf{s}$,$\mathbf{p}^+$, $\rho_\mathbf{Z}$) for every partition $p$;
+	\item ($\mathbf{s}$,$\mathbf{p}^-$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$;
+	\item ($\mathbf{p}^+$,$\mathbf{x}_{p,z}$, 1) for every partition $p$ and zone $z$;
+	\item ($\mathbf{p}^-$,$\mathbf{x}_{p,z}$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$ and zone $z$;
+	\item ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) for every partition $p$, zone $z$ and node $n\in z$;
+	\item ($\mathbf{n}$, $\mathbf{t}$, $\lfloor c_n/s \rfloor$) for every node $n$.
+\end{itemize}
+
+\begin{figure}
+	\centering
+	\includegraphics[width=\linewidth]{figures/flow_graph_param}
+	\caption{An example of graph $G(s)$. Arcs are oriented from left to right, and unlabeled arcs have capacity 1. In this example, nodes $n_1,n_2,n_3$ belong to zone $z_1$, and nodes $n_4,n_5$ belong to zone $z_2$.}
+	\label{fig:flowgraph}
+\end{figure}
+
+In the following complexity calculations, we will use the number of vertices and edges of $G$. Remark from now that $\# V = O(PZ)$ and $\# E = O(PN)$.
+
+\begin{proposition}
+	An assignment $\alpha$ is realizable with partition size $s$ and the redundancy constraints $(\rho_\mathbf{N},\rho_\mathbf{Z})$ if and only if there exists a maximal flow function $f$ in $G$ with total flow $\rho_\mathbf{N}P$, such that the arcs ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) used are exactly those for which $p$ is associated to $n$ in $\alpha$.
+\end{proposition}
+\begin{proof}
+	Given such flow $f$, we can reconstruct a candidate $\alpha$. In $f$, the flow passing through $\mathbf{p^+}$ and $\mathbf{p^-}$ is $\rho_\mathbf{N}$, and since the outgoing capacity of every $\mathbf{x}_{p,z}$ is 1, every partition is associated to $\rho_\mathbf{N}$ distinct nodes. The fraction $\rho_\mathbf{Z}$ of the flow passing through every $\mathbf{p^+}$ must be spread over as many distinct zones as every arc outgoing from $\mathbf{p^+}$ has capacity 1. So the reconstructed $\alpha$ verifies the redundancy constraints. For every node $n$, the flow between $\mathbf{n}$ and $\mathbf{t}$ corresponds to the number of partitions associated to $n$. By construction of $f$, this does not exceed $\lfloor c_n/s \rfloor$. We assumed that the partition size is $s$, hence this association does not exceed the storage capacity of the nodes.
+	
+	In the other direction, given an assignment $\alpha$, one can similarly check that the facts that $\alpha$ respects the redundancy constraints, and the storage capacities of the nodes, are necessary condition to construct a maximal flow function $f$.
+\end{proof}
+
+\textbf{Implementation remark:} In the flow algorithm, while exploring the graph, we explore the neighbours of every vertex in a random order to heuristically spread the associations between nodes and partitions.
+
+\subsubsection*{Algorithm}
+With this result mind, we can describe the first step of our algorithm. All divisions are supposed to be integer divisions.
+\begin{algorithmic}[1]
+	\Function{Compute Partition Size}{$\mathbf{N}$, $\mathbf{Z}$, $\mathbf{P}$, $(c_n)_{n\in \mathbf{N}}$, $\rho_\mathbf{N}$, $\rho_\mathbf{Z}$}
+	
+	\State Build the graph $G=G(s=1)$
+	\State $ f \leftarrow$ \Call{Maximal flow}{$G$}
+	\If{$f.\mathrm{total flow} < \rho_\mathbf{N}P$}
+	
+	\State \Return Error: capacities too small or constraints too strong.
+	\EndIf
+	
+	\State $s^- \leftarrow 1$
+	\State $s^+ \leftarrow 1+\frac{1}{\rho_\mathbf{N}}\sum_{n \in \mathbf{N}} c_n$
+	
+	\While{$s^-+1 < s^+$}
+	\State Build the graph $G=G(s=(s^-+s^+)/2)$
+	\State $ f \leftarrow$ \Call{Maximal flow}{$G$}
+	\If{$f.\mathrm{total flow} < \rho_\mathbf{N}P$}
+	\State $s^+ \leftarrow (s^- + s^+)/2$
+	\Else
+	\State $s^- \leftarrow (s^- + s^+)/2$
+	\EndIf
+	\EndWhile
+	
+	\State \Return $s^-$
+	\EndFunction
+\end{algorithmic}
+
+\subsubsection*{Complexity}
+
+To compute the maximal flow, we use Dinic's algorithm. Its complexity on general graphs is $O(\#V^2 \#E)$, but on graphs with edge capacity bounded by a constant, it turns out to be $O(\#E^{3/2})$. The graph $G$ does not fall in this case since the capacities of the arcs incoming to $\mathbf{t}$ are far from bounded. However, the proof of this complexity function works readily for graphs where we only ask the edges \emph{not} incoming to the sink $\mathbf{t}$ to have their capacities bounded by a constant. One can find the proof of this claim in \cite[Section 2]{even1975network}.
+The dichotomy adds a logarithmic factor $\log (C)$ where $C=\sum_{n \in \mathbf{N}} c_n$ is the total capacity of the cluster. The total complexity of this first function is hence 
+$O(\#E^{3/2}\log C ) = O\big((PN)^{3/2} \log C\big)$.
+
+\subsubsection*{Metrics}
+We can display the discrepancy between the computed $s^*$ and the best size we could have hoped for the given total capacity, that is $C/\rho_\mathbf{N}$.
+
+\subsection{Computation of a candidate assignment}
+
+Now that we have the optimal partition size $s^*$, to compute a candidate assignment it would be enough to compute a maximal flow function $f$ on $G(s^*)$. This is what we do if there is no former assignation $\alpha'$.
+
+If there is some $\alpha'$, we add a step that will heuristically help to obtain a candidate $\alpha$ closer to $\alpha'$. We fist compute a flow function $\tilde{f}$ that uses only the partition-to-node associations appearing in $\alpha'$. Most likely, $\tilde{f}$ will not be a maximal flow of $G(s^*)$. In Dinic's algorithm, we can start from a non maximal flow function and then discover improving paths. This is what we do by starting from $\tilde{f}$. The hope\footnote{This is only a hope, because one can find examples where the construction of $f$ from $\tilde{f}$ produces an assignment $\alpha$ that is not as close as possible to $\alpha'$.} is that the final flow function $f$ will tend to keep the associations appearing in $\tilde{f}$.
+
+More formally, we construct the graph $G_{|\alpha'}$ from $G$ by removing all the arcs $(\mathbf{x}_{p,z},\mathbf{n}, 1)$ where $p$ is not associated to $n$ in $\alpha'$. We compute a maximal flow function $\tilde{f}$ in $G_{|\alpha'}$. The flow $\tilde{f}$ is also a valid (most likely non maximal) flow function on $G$. We compute a maximal flow function $f$ on $G$ by starting Dinic's algorithm on $\tilde{f}$.
+
+\subsubsection*{Algorithm}
+\begin{algorithmic}[1]
+	\Function{Compute Candidate Assignment}{$G$, $\alpha'$}
+	\State Build the graph $G_{|\alpha'}$
+	\State $ \tilde{f} \leftarrow$ \Call{Maximal flow}{$G_{|\alpha'}$}
+	\State $ f \leftarrow$ \Call{Maximal flow from flow}{$G$, $\tilde{f}$}
+	\State \Return $f$
+	\EndFunction
+\end{algorithmic}
+
+~ 
+
+\textbf{Remark:} The function ``Maximal flow'' can be just seen as the function ``Maximal flow from flow'' called with the zero flow function as starting flow.
+
+\subsubsection*{Complexity}
+With the considerations of the last section, we have the complexity of the Dinic's algorithm $O(\#E^{3/2}) = O((PN)^{3/2})$.
+
+\subsubsection*{Metrics}
+
+We can display the flow value of $\tilde{f}$, which is an upper bound of the distance between $\alpha$ and $\alpha'$. It might be more a Debug level display than Info.
+
+\subsection{Minimization of the transfer load}
+
+Now that we have a candidate flow function $f$, we want to modify it to make its corresponding assignation $\alpha$ as close as possible to $\alpha'$. Denote by $f'$ the maximal flow corresponding to $\alpha'$, and let $d(f, \alpha')=d(f, f'):=d(\alpha,\alpha')$\footnote{It is the number of arcs of type $(\mathbf{x}_{p,z},\mathbf{n})$ saturated in one flow and not in the other.}. 
+We want to build a sequence $f=f_0, f_1, f_2 \dots$ of maximal flows such that $d(f_i, \alpha')$ decreases as $i$ increases. The distance being a non-negative integer, this sequence of flow functions must be finite. We now explain how to find some improving $f_{i+1}$ from $f_i$.
+
+For any maximal flow $f$ in $G$, we define the oriented weighted graph $G_f=(V, E_f)$ as follows. The vertices of $G_f$ are the same as the vertices of $G$. $E_f$ contains the arc $(v_1,v_2, w)$ between vertices $v_1,v_2\in V$ with weight $w$ if and only if the arc $(v_1,v_2)$ is not saturated in $f$ (i.e. $c(v_1,v_2)-f(v_1,v_2) \ge 1$, we also consider reversed arcs). The weight $w$ is: 
+\begin{itemize}
+	\item  $-1$  if $(v_1,v_2)$ is of type $(\mathbf{x}_{p,z},\mathbf{n})$ or $(\mathbf{x}_{p,z},\mathbf{n})$ and is saturated in only one of the two flows $f,f'$;
+	\item $+1$  if $(v_1,v_2)$ is of type $(\mathbf{x}_{p,z},\mathbf{n})$ or $(\mathbf{x}_{p,z},\mathbf{n})$ and is saturated in either both or none of the two flows $f,f'$;
+	\item $0$ otherwise.
+\end{itemize}
+
+If $\gamma$ is a simple cycle of arcs in $G_f$, we define its weight $w(\gamma)$ as the sum of the weights of its arcs. We can add $+1$ to the value of $f$ on the arcs of $\gamma$, and by construction of $G_f$ and the fact that $\gamma$ is a cycle, the function that we get is still a valid flow function on $G$, it is maximal as it has the same flow value as $f$. We denote this new function $f+\gamma$.
+
+\begin{proposition}
+	Given a maximal flow $f$ and a simple cycle $\gamma$ in $G_f$, we have $d(f+\gamma, f') - d(f,f') = w(\gamma)$.
+\end{proposition}
+\begin{proof}
+	Let $X$ be the set of arcs of type $(\mathbf{x}_{p,z},\mathbf{n})$. Then we can express $d(f,f')$ as
+	\begin{align*}
+		d(f,f') & = \#\{e\in X ~|~ f(e)\neq f'(e)\}
+		= \sum_{e\in X} 1_{f(e)\neq f'(e)} \\
+		& = \frac{1}{2}\big( \#X + \sum_{e\in X} 1_{f(e)\neq f'(e)} - 1_{f(e)= f'(e)} \big).
+	\end{align*}
+	We can express the cycle weight as
+	\begin{align*}
+		w(\gamma) &  = \sum_{e\in X, e\in \gamma} - 1_{f(e)\neq f'(e)} + 1_{f(e)= f'(e)}.
+	\end{align*}
+	Remark that since we passed on unit of flow in $\gamma$ to construct $f+\gamma$, we have for any $e\in X$, $f(e)=f'(e)$ if and only if $(f+\gamma)(e) \neq f'(e)$.
+	Hence
+	\begin{align*}
+		w(\gamma) &  = \frac{1}{2}(w(\gamma) + w(\gamma)) \\
+		&= \frac{1}{2} \Big( 
+		\sum_{e\in X, e\in \gamma} - 1_{f(e)\neq f'(e)} +  1_{f(e)= f'(e)} \\
+		& \qquad +
+		\sum_{e\in X, e\in \gamma} 1_{(f+\gamma)(e)\neq f'(e)} +  1_{(f+\gamma)(e)= f'(e)}
+		\Big).
+	\end{align*}
+	Plugging this in the previous equation, we find that 
+	$$d(f,f')+w(\gamma) = d(f+\gamma, f').$$
+\end{proof}
+
+This result suggests that given some flow $f_i$, we just need to find a negative cycle $\gamma$ in $G_{f_i}$ to construct $f_{i+1}$ as $f_i+\gamma$. The following proposition ensures that this greedy strategy reaches an optimal flow. 
+
+\begin{proposition}
+	For any maximal flow $f$, $G_f$ contains a negative cycle if and only if there exists a maximal flow $f^*$ in $G$ such that $d(f^*, f') < d(f, f')$.
+\end{proposition}
+\begin{proof}
+	Suppose that there is such flow $f^*$. Define the oriented multigraph $M_{f,f^*}=(V,E_M)$ with the same vertex set $V$ as in $G$, and for every $v_1,v_2 \in V$, $E_M$ contains $(f^*(v_1,v_2) - f(v_1,v_2))_+$  copies of the arc $(v_1,v_2)$. For every vertex $v$, its total degree (meaning its outer degree minus its inner degree) is equal to 
+	\begin{align*}
+		\deg v & = \sum_{u\in V} (f^*(v,u) - f(v,u))_+ - \sum_{u\in V} (f^*(u,v) - f(u,v))_+  \\
+		& = \sum_{u\in V} f^*(v,u) - f(v,u) = \sum_{u\in V} f^*(v,u) - \sum_{u\in V}  f(v,u).
+	\end{align*}
+	The last two sums are zero for any inner vertex since $f,f^*$ are flows, and they are equal on the source and sink since the two flows are both maximal and have hence the same value. Thus, $\deg v = 0$ for every vertex $v$.
+	
+	This implies that the multigraph $M_{f,f^*}$ is the union of disjoint simple cycles. $f$ can be transformed into $f^*$ by pushing a mass 1 along all these cycles in any order. Since $d(f^*, f')<d(f,f')$, there must exists one of these simple cycles $\gamma$ with $d(f+\gamma, f') < d(f, f')$. Finally, since we can push a mass in $f$ along $\gamma$, it must appear in $G_f$. Hence $\gamma$ is a cycle of $G_f$ with negative weight.
+\end{proof}
+
+In the next section we describe the corresponding algorithm. Instead of discovering only one cycle, we are allowed to discover a set $\Gamma$ of disjoint negative cycles. 
+
+\subsubsection*{Algorithm}
+\begin{algorithmic}[1]
+	\Function{Minimize transfer load}{$G$, $f$, $\alpha'$}
+	\State Build the graph $G_f$
+	\State $\Gamma \leftarrow$ \Call{Detect Negative Cycles}{$G_f$}
+	\While{$\Gamma \neq \emptyset$}
+	\ForAll{$\gamma \in \Gamma$}
+	\State $f \leftarrow f+\gamma$
+	\EndFor
+	\State Update $G_f$
+	\State $\Gamma \leftarrow$ \Call{Detect Negative Cycles}{$G_f$}
+	\EndWhile
+	\State \Return $f$
+	\EndFunction
+\end{algorithmic}
+
+\subsubsection*{Complexity}
+The distance $d(f,f')$ is bounded by the maximal number of differences in the associated assignment. If these assignment are totally disjoint, this distance is $2\rho_N P$. At every iteration of the While loop, the distance decreases, so there is at most $O(\rho_N P) = O(P)$ iterations.
+
+The detection of negative cycle is done with the Bellman-Ford algorithm, whose complexity should normally be $O(\#E\#V)$. In our case, it amounts to $O(P^2ZN)$. Multiplied by the complexity of the outer loop, it amounts to $O(P^3ZN)$ which is a lot when the number of partitions and nodes starts to be large. To avoid that, we adapt the Bellman-Ford algorithm.
+
+The Bellman-Ford algorithm runs $\#V$ iterations of an outer loop, and an inner loop over $E$. The idea is to compute the shortest paths from a source vertex $v$ to all other vertices. After $k$ iterations of the outer loop, the algorithm has computed all shortest path of length at most $k$. All simple paths have length at most $\#V-1$, so if there is an update in the last iteration of the loop, it means that there is a negative cycle in the graph. The observation that will enable us to improve the complexity is the following:
+
+\begin{proposition}
+	In the graph $G_f$ (and $G$), all simple paths have a length at most $4N$.
+\end{proposition}
+\begin{proof}
+	Since $f$ is a maximal flow, there is no outgoing edge from $\mathbf{s}$ in $G_f$. One can thus check than any simple path of length 4 must contain at least two node of type $\mathbf{n}$. Hence on a path, at most 4 arcs separate two successive nodes of type $\mathbf{n}$. 
+\end{proof}
+
+Thus, in the absence of negative cycles, shortest paths in $G_f$ have length at most $4N$. So we can do only $4N+1$ iterations of the outer loop in the Bellman-Ford algorithm. This makes the complexity of the detection of one set of cycle to be $O(N\#E) = O(N^2 P)$.
+
+With this improvement, the complexity of the whole algorithm is, in the worst case, $O(N^2P^2)$. However, since we detect several cycles at once and we start with a flow that might be close to the previous one, the number of iterations of the outer loop might be smaller in practice.
+
+
+
+\subsubsection*{Metrics}
+We can display the node and zone utilization ratio, by dividing the flow passing through them divided by their outgoing capacity. In particular, we can pinpoint saturated nodes and zones (i.e. used at their full potential).
+
+We can display the distance to the previous assignment, and the number of partition transfers.
+
+
+\bibliography{optimal_layout} 
+\bibliographystyle{ieeetr}
+
+\end{document}
+
+
+
@@ -0,0 +1,11 @@
+
+@article{even1975network,
+	title={Network flow and testing graph connectivity},
+	author={Even, Shimon and Tarjan, R Endre},
+	journal={SIAM journal on computing},
+	volume={4},
+	number={4},
+	pages={507--518},
+	year={1975},
+	publisher={SIAM}
+}
@@ -0,0 +1,709 @@
+\documentclass[]{article}
+
+\usepackage{amsmath,amssymb}
+\usepackage{amsthm}
+
+\usepackage{graphicx,xcolor}
+
+\usepackage{algorithm,algpseudocode,float} 
+
+\renewcommand\thesubsubsection{\Alph{subsubsection})}
+
+\newtheorem{proposition}{Proposition}
+
+%opening
+\title{Optimal partition assignment in Garage}
+\author{Mendes}
+
+\begin{document}
+
+\maketitle
+
+\section{Introduction}
+
+\subsection{Context}
+
+Garage is an open-source distributed storage service blablabla$\dots$
+
+Every object to be stored in the system falls in a partition given by the last $k$ bits of its hash. There are $P=2^k$ partitions. Every partition will be stored on distinct nodes of the system. The goal of the assignment of partitions to nodes is to ensure (nodes and zone) redundancy and to be as efficient as possible.
+
+\subsection{Formal description of the problem}
+
+We are given a set of nodes $\mathbf{N}$ and a set of zones $\mathbf{Z}$. Every node $n$ has a non-negative storage capacity $c_n\ge 0$ and belongs to a zone $z\in \mathbf{Z}$. We are also given a number of partition $P>0$ (typically $P=256$).
+
+We would like to compute an assignment of nodes to partitions. We will impose some redundancy constraints to this assignment, and under these constraints, we want our system to have the largest storage capacity possible. To link storage capacity to partition assignment, we make the following assumption:
+\begin{equation}
+	\tag{H1}
+	\text{\emph{All partitions have the same size $s$.}}
+\end{equation}
+This assumption is justified by the dispersion of the hashing function, when the number of partitions is small relative to the number of stored large objects.
+
+Every node $n$ wille store some number $k_n$ of partitions. Hence the partitions stored by $n$ (and hence all partitions by our assumption) have there size bounded by $c_n/k_n$. This remark leads us to define the optimal size that we will want to maximize:
+
+\begin{equation}
+	\label{eq:optimal}
+	\tag{OPT}
+s^* = \min_{n \in N} \frac{c_n}{k_n}.
+\end{equation}
+
+When the capacities of the nodes are updated (this includes adding or removing a node), we want to update the assignment as well. However, transferring the data between nodes has a cost and we would like to limit the number of changes in the assignment. We make the following assumption:
+\begin{equation}
+	\tag{H2}
+	\text{\emph{Updates of capacity happens rarely relatively to object storing.}}
+\end{equation}
+This assumption justifies that when we compute the new assignment, it is worth to optimize the partition size \eqref{eq:optimal} first, and then, among the possible optimal solution, to try to minimize the number of partition transfers.
+
+For now, in the following, we ask the following redundancy constraint:
+
+\textbf{Parametric node and zone redundancy:} Given two integer parameters $1\le \rho_\mathbf{Z} \le \rho_\mathbf{N}$, we ask every partition to be stored on $\rho_\mathbf{N}$ distinct nodes, and these nodes must belong to at least $\rho_\mathbf{Z}$ distinct zones.
+
+
+\textbf{Mode 3-strict:}  every partition needs to be assignated to three nodes belonging to three different zones.
+
+\textbf{Mode 3:} every partition needs to be assignated to three nodes. We try to spread the three nodes over different zones as much as possible.
+
+\textbf{Warning:} This is a working document written incrementaly. The last version of the algorithm is the \textbf{parametric assignment} described in the next section.
+
+
+\section{Computation of a parametric assignment}
+\textbf{Attention : }We change notations in this section.
+
+Notations : let $P$ be the number of partitions, $N$ the number of nodes, $Z$ the number of zones. Let $\mathbf{P,N,Z}$ be the label sets of, respectively, partitions, nodes and zones.
+Let $s^*$ be the largest partition size achievable with the redundancy constraints. Let $(c_n)_{n\in \mathbf{N}}$ be the storage capacity of every node. 
+
+In this section, we propose a third specification of the problem. The user inputs two redundancy parameters $1\le \rho_\mathbf{Z} \le \rho_\mathbf{N}$. We compute an assignment $\alpha = (\alpha_p^1, \ldots, \alpha_p^{\rho_\mathbf{N}})_{p\in \mathbf{P}}$ such that every partition $p$ is associated to $\rho_\mathbf{N}$ distinct nodes $\alpha_p^1, \ldots, \alpha_p^{\rho_\mathbf{N}}$ and these nodes belong to at least $\rho_\mathbf{Z}$ distinct zones.
+
+If the layout contained a previous assignment $\alpha'$, we try to minimize the amount of data to transfer during the layout update by making $\alpha$ as close as possible to $\alpha'$.
+
+In the following subsections, we describe the successive steps of the algorithm we propose to compute $\alpha$.
+
+\subsubsection*{Algorithm}
+
+\begin{algorithmic}[1]
+	\Function{Compute Layout}{$\mathbf{N}$, $\mathbf{Z}$, $\mathbf{P}$, $(c_n)_{n\in \mathbf{N}}$, $\rho_\mathbf{N}$, $\rho_\mathbf{Z}$, $\alpha'$}
+	\State $s^* \leftarrow$ \Call{Compute Partition Size}{$\mathbf{N}$, $\mathbf{Z}$, $\mathbf{P}$, $(c_n)_{n\in \mathbf{N}}$, $\rho_\mathbf{N}$, $\rho_\mathbf{Z}$}
+	\State $G \leftarrow G(s^*)$
+	\State $f \leftarrow$ 	\Call{Compute Candidate Assignment}{$G$, $\alpha'$}
+	\State $f^* \leftarrow$ 	\Call{Minimize transfer load}{$G$, $f$, $\alpha'$}
+	\State Build $\alpha^*$ from $f^*$
+	\State \Return $\alpha^*$
+	\EndFunction
+\end{algorithmic}
+
+\subsubsection*{Complexity}
+As we will see in the next sections, the worst case complexity of this algorithm is $O(P^2 N^2)$. The minimization of transfer load is the most expensive step, and it can run with a timeout since it is only an optimization step. Without this step (or with a smart timeout), the worst cas complexity can be $O((PN)^{3/2}\log C)$ where $C$ is the total storage capacity of the cluster. 
+
+\subsection{Determination of the partition size $s^*$}
+
+Again, we will represent an assignment $\alpha$ as a flow in a specific graph $G$. We will not compute the optimal partition size $s^*$ a priori, but we will determine it by dichotomy, as the largest size $s$ such that the maximal flow achievable on $G=G(s)$ has value $\rho_\mathbf{N}P$. We will assume that the capacities are given in a small enough unit (say, Megabytes), and we will determine $s^*$ at the precision of the given unit.
+
+Given some candidate size value $s$, we describe the oriented weighted graph $G=(V,E)$ with vertex set $V$ arc set $E$.
+
+The set of vertices $V$ contains the source $\mathbf{s}$, the sink $\mathbf{t}$, vertices 
+$\mathbf{p^+, p^-}$ for every partition $p$, vertices $\mathbf{x}_{p,z}$ for every partition $p$ and zone $z$, and vertices $\mathbf{n}$ for every node $n$. 
+
+The set of arcs $E$ contains:
+\begin{itemize}
+	\item ($\mathbf{s}$,$\mathbf{p}^+$, $\rho_\mathbf{Z}$) for every partition $p$;
+	\item ($\mathbf{s}$,$\mathbf{p}^-$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$;
+	\item ($\mathbf{p}^+$,$\mathbf{x}_{p,z}$, 1) for every partition $p$ and zone $z$;
+	\item ($\mathbf{p}^-$,$\mathbf{x}_{p,z}$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$ and zone $z$;
+	\item ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) for every partition $p$, zone $z$ and node $n\in z$;
+	\item ($\mathbf{n}$, $\mathbf{t}$, $\lfloor c_n/s \rfloor$) for every node $n$.
+\end{itemize}
+
+In the following complexity calculations, we will use the number of vertices and edges of $G$. Remark from now that $\# V = O(PZ)$ and $\# E = O(PN)$.
+
+\begin{proposition}
+	An assignment $\alpha$ is realizable with partition size $s$ and the redundancy constraints $(\rho_\mathbf{N},\rho_\mathbf{Z})$ if and only if there exists a maximal flow function $f$ in $G$ with total flow $\rho_\mathbf{N}P$, such that the arcs ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) used are exactly those for which $p$ is associated to $n$ in $\alpha$.
+\end{proposition}
+\begin{proof}
+	Given such flow $f$, we can reconstruct a candidate $\alpha$. In $f$, the flow passing through $\mathbf{p^+}$ and $\mathbf{p^-}$ is $\rho_\mathbf{N}$, and since the outgoing capacity of every $\mathbf{x}_{p,z}$ is 1, every partition is associated to $\rho_\mathbf{N}$ distinct nodes. The fraction $\rho_\mathbf{Z}$ of the flow passing through every $\mathbf{p^+}$ must be spread over as many distinct zones as every arc outgoing from $\mathbf{p^+}$ has capacity 1. So the reconstructed $\alpha$ verifies the redundancy constraints. For every node $n$, the flow between $\mathbf{n}$ and $\mathbf{t}$ corresponds to the number of partitions associated to $n$. By construction of $f$, this does not exceed $\lfloor c_n/s \rfloor$. We assumed that the partition size is $s$, hence this association does not exceed the storage capacity of the nodes.
+	
+	In the other direction, given an assignment $\alpha$, one can similarly check that the facts that $\alpha$ respects the redundancy constraints, and the storage capacities of the nodes, are necessary condition to construct a maximal flow function $f$.
+\end{proof}
+
+\textbf{Implementation remark:} In the flow algorithm, while exploring the graph, we explore the neighbours of every vertex in a random order to heuristically spread the association between nodes and partitions.
+
+\subsubsection*{Algorithm}
+With this result mind, we can describe the first step of our algorithm. All divisions are supposed to be integer division.
+\begin{algorithmic}[1]
+	\Function{Compute Partition Size}{$\mathbf{N}$, $\mathbf{Z}$, $\mathbf{P}$, $(c_n)_{n\in \mathbf{N}}$, $\rho_\mathbf{N}$, $\rho_\mathbf{Z}$}
+	
+	\State Build the graph $G=G(s=1)$
+	\State $ f \leftarrow$ \Call{Maximal flow}{$G$}
+	\If{$f.\mathrm{total flow} < \rho_\mathbf{N}P$}
+	
+	\State \Return Error: capacities too small or constraints too strong.
+	\EndIf
+	
+	\State $s^- \leftarrow 1$
+	\State $s^+ \leftarrow 1+\frac{1}{\rho_\mathbf{N}}\sum_{n \in \mathbf{N}} c_n$
+	
+	\While{$s^-+1 < s^+$}
+	\State Build the graph $G=G(s=(s^-+s^+)/2)$
+	\State $ f \leftarrow$ \Call{Maximal flow}{$G$}
+	\If{$f.\mathrm{total flow} < \rho_\mathbf{N}P$}
+	\State $s^+ \leftarrow (s^- + s^+)/2$
+	\Else
+	\State $s^- \leftarrow (s^- + s^+)/2$
+	\EndIf
+	\EndWhile
+	
+	\State \Return $s^-$
+	\EndFunction
+\end{algorithmic}
+
+\subsubsection*{Complexity}
+
+To compute the maximal flow, we use Dinic's algorithm. Its complexity on general graphs is $O(\#V^2 \#E)$, but on graphs with edge capacity bounded by a constant, it turns out to be $O(\#E^{3/2})$. The graph $G$ does not fall in this case since the capacities of the arcs incoming to $\mathbf{t}$ are far from bounded. However, the proof of this complexity works readily for graph where we only ask the edges \emph{not} incoming to the sink $\mathbf{t}$ to have their capacities bounded by a constant. One can find the proof of this claim in \cite[Section 2]{even1975network}.
+The dichotomy adds a logarithmic factor $\log (C)$ where $C=\sum_{n \in \mathbf{N}} c_n$ is the total capacity of the cluster. The total complexity of this first function is hence 
+$O(\#E^{3/2}\log C ) = O\big((PN)^{3/2} \log C\big)$.
+
+\subsubsection*{Metrics}
+We can display the discrepancy between the computed $s^*$ and the best size we could hope for a given total capacity, that is $C/\rho_\mathbf{N}$.
+
+\subsection{Computation of a candidate assignment}
+
+Now that we have the optimal partition size $s^*$, to compute a candidate assignment, it would be enough to compute a maximal flow function $f$ on $G(s^*)$. This is what we do if there was no previous assignment $\alpha'$.
+
+If there was some $\alpha'$, we add a step that will heuristically help to obtain a candidate $\alpha$ closer to $\alpha'$. to do so, we fist compute a flow function $\tilde{f}$ that uses only the partition-to-node association appearing in $\alpha'$. Most likely, $\tilde{f}$ will not be a maximal flow of $G(s^*)$. In Dinic's algorithm, we can start from a non maximal flow function and then discover improving paths. This is what we do in starting from $\tilde{f}$. The hope\footnote{This is only a hope, because one can find examples where the construction of $f$ from $\tilde{f}$ produces an assignment $\alpha$ that is not as close as possible to $\alpha'$.} is that the final flow function $f$ will tend to keep the associations appearing in $\tilde{f}$.
+
+More formally, we construct the graph $G_{|\alpha'}$ from $G$ by removing all the arcs $(\mathbf{x}_{p,z},\mathbf{n}, 1)$ where $p$ is not associated to $n$ in $\alpha'$. We compute a maximal flow function $\tilde{f}$ in $G_{|\alpha'}$. $\tilde{f}$ is also a valid (most likely non maximal) flow function in $G$. We compute a maximal flow function $f$ on $G$ by starting Dinic's algorithm on $\tilde{f}$.
+
+\subsubsection*{Algorithm}
+\begin{algorithmic}[1]
+	\Function{Compute Candidate Assignment}{$G$, $\alpha'$}
+	\State Build the graph $G_{|\alpha'}$
+	\State $ \tilde{f} \leftarrow$ \Call{Maximal flow}{$G_{|\alpha'}$}
+	\State $ f \leftarrow$ \Call{Maximal flow from flow}{$G$, $\tilde{f}$}
+	\State \Return $f$
+	\EndFunction
+\end{algorithmic}
+
+\textbf{Remark:} The function ``Maximal flow'' can be just seen as the function ``Maximal flow from flow'' called with the zero flow function as starting flow.
+
+\subsubsection*{Complexity}
+From the consideration of the last section, we have the complexity of the Dinic's algorithm $O(\#E^{3/2}) = O((PN)^{3/2})$.
+
+\subsubsection*{Metrics}
+
+We can display the flow value of $\tilde{f}$, which is an upper bound of the distance between $\alpha$ and $\alpha'$. It might be more a Debug level display than Info.
+
+\subsection{Minimization of the transfer load}
+
+Now that we have a candidate flow function $f$, we want to modify it to make its associated assignment as close as possible to $\alpha'$. Denote by $f'$ the maximal flow associated to $\alpha'$, and let $d(f, f')$ be distance between the associated assignments\footnote{It is the number of arcs of type $(\mathbf{x}_{p,z},\mathbf{n})$ saturated in one flow and not in the other.}. 
+We want to build a sequence $f=f_0, f_1, f_2 \dots$ of maximal flows such that $d(f_i, \alpha')$ decreases as $i$ increases. The distance being a non-negative integer, this sequence of flow functions must be finite. We now explain how to find some improving $f_{i+1}$ from $f_i$.
+
+For any maximal flow $f$ in $G$, we define the oriented weighted graph $G_f=(V, E_f)$ as follows. The vertices of $G_f$ are the same as the vertices of $G$. $E_f$ contains the arc $(v_1,v_2, w)$ between vertices $v_1,v_2\in V$ with weight $w$ if and only if the arc $(v_1,v_2)$ is not saturated in $f$ (i.e. $c(v_1,v_2)-f(v_1,v_2) \ge 1$, we also consider reversed arcs). The weight $w$ is: 
+\begin{itemize}
+	\item  $-1$  if $(v_1,v_2)$ is of type $(\mathbf{x}_{p,z},\mathbf{n})$ or $(\mathbf{x}_{p,z},\mathbf{n})$ and is saturated in only one of the two flows $f,f'$;
+	\item $+1$  if $(v_1,v_2)$ is of type $(\mathbf{x}_{p,z},\mathbf{n})$ or $(\mathbf{x}_{p,z},\mathbf{n})$ and is saturated in either both or none of the two flows $f,f'$;
+	\item $0$ otherwise.
+\end{itemize}
+
+If $\gamma$ is a simple cycle of arcs in $G_f$, we define its weight $w(\gamma)$ as the sum of the weights of its arcs. We can add $+1$ to the value of $f$ on the arcs of $\gamma$, and by construction of $G_f$ and the fact that $\gamma$ is a cycle, the function that we get is still a valid flow function on $G$, it is maximal as it has the same flow value as $f$. We denote this new function $f+\gamma$.
+
+\begin{proposition}
+	Given a maximal flow $f$ and a simple cycle $\gamma$ in $G_f$, we have $d(f+\gamma, f') - d(f,f') = w(\gamma)$.
+\end{proposition}
+\begin{proof}
+	Let $X$ be the set of arcs of type $(\mathbf{x}_{p,z},\mathbf{n})$. Then we can express $d(f,f')$ as
+	\begin{align*}
+		d(f,f') & = \#\{e\in X ~|~ f(e)\neq f'(e)\}
+		= \sum_{e\in X} 1_{f(e)\neq f'(e)} \\
+		& = \frac{1}{2}\big( \#X + \sum_{e\in X} 1_{f(e)\neq f'(e)} - 1_{f(e)= f'(e)} \big).
+	\end{align*}
+	We can express the cycle weight as
+	\begin{align*}
+		w(\gamma) &  = \sum_{e\in X, e\in \gamma} - 1_{f(e)\neq f'(e)} + 1_{f(e)= f'(e)}.
+	\end{align*}
+	Remark that since we passed on unit of flow in $\gamma$ to construct $f+\gamma$, we have for any $e\in X$, $f(e)=f'(e)$ if and only if $(f+\gamma)(e) \neq f'(e)$.
+	Hence
+	\begin{align*}
+		w(\gamma) &  = \frac{1}{2}(w(\gamma) + w(\gamma)) \\
+		&= \frac{1}{2} \Big( 
+		\sum_{e\in X, e\in \gamma} - 1_{f(e)\neq f'(e)} +  1_{f(e)= f'(e)} \\
+		& \qquad +
+		\sum_{e\in X, e\in \gamma} 1_{(f+\gamma)(e)\neq f'(e)} +  1_{(f+\gamma)(e)= f'(e)}
+		\Big).
+	\end{align*}
+	Plugging this in the previous equation, we find that 
+	$$d(f,f')+w(\gamma) = d(f+\gamma, f').$$
+\end{proof}
+
+This result suggests that given some flow $f_i$, we just need to find a negative cycle $\gamma$ in $G_{f_i}$ to construct $f_{i+1}$ as $f_i+\gamma$. The following proposition ensures that this greedy strategy reaches an optimal flow. 
+
+\begin{proposition}
+	For any maximal flow $f$, $G_f$ contains a negative cycle if and only if there exists a maximal flow $f^*$ in $G$ such that $d(f^*, f') < d(f, f')$.
+\end{proposition}
+\begin{proof}
+	Suppose that there is such flow $f^*$. Define the oriented multigraph $M_{f,f^*}=(V,E_M)$ with the same vertex set $V$ as in $G$, and for every $v_1,v_2 \in V$, $E_M$ contains $(f^*(v_1,v_2) - f(v_1,v_2))_+$  copies of the arc $(v_1,v_2)$. For every vertex $v$, its total degree (meaning its outer degree minus its inner degree) is equal to 
+	\begin{align*}
+		\deg v & = \sum_{u\in V} (f^*(v,u) - f(v,u))_+ - \sum_{u\in V} (f^*(u,v) - f(u,v))_+  \\
+		& = \sum_{u\in V} f^*(v,u) - f(v,u) = \sum_{u\in V} f^*(v,u) - \sum_{u\in V}  f(v,u).
+	\end{align*}
+	The last two sums are zero for any inner vertex since $f,f^*$ are flows, and they are equal on the source and sink since the two flows are both maximal and have hence the same value. Thus, $\deg v = 0$ for every vertex $v$.
+	
+	This implies that the multigraph $M_{f,f^*}$ is the union of disjoint simple cycles. $f$ can be transformed into $f^*$ by pushing a mass 1 along all these cycles in any order. Since $d(f^*, f')<d(f,f')$, there must exists one of these simple cycles $\gamma$ with $d(f+\gamma, f') < d(f, f')$. Finally, since we can push a mass in $f$ along $\gamma$, it must appear in $G_f$. Hence $\gamma$ is a cycle of $G_f$ with negative weight.
+\end{proof}
+
+In the next section we describe the corresponding algorithm. Instead of discovering only one cycle, we are allowed to discover a set $\Gamma$ of disjoint negative cycles. 
+
+\subsubsection*{Algorithm}
+\begin{algorithmic}[1]
+	\Function{Minimize transfer load}{$G$, $f$, $\alpha'$}
+	\State Build the graph $G_f$
+	\State $\Gamma \leftarrow$ \Call{Detect Negative Cycles}{$G_f$}
+	\While{$\Gamma \neq \emptyset$}
+	\ForAll{$\gamma \in \Gamma$}
+	\State $f \leftarrow f+\gamma$
+	\EndFor
+	\State Update $G_f$
+	\State $\Gamma \leftarrow$ \Call{Detect Negative Cycles}{$G_f$}
+	\EndWhile
+	\State \Return $f$
+	\EndFunction
+\end{algorithmic}
+
+\subsubsection*{Complexity}
+The distance $d(f,f')$ is bounded by the maximal number of differences in the associated assignment. If these assignment are totally disjoint, this distance is $2\rho_N P$. At every iteration of the While loop, the distance decreases, so there is at most $O(\rho_N P) = O(P)$ iterations.
+
+The detection of negative cycle is done with the Bellman-Ford algorithm, whose complexity should normally be $O(\#E\#V)$. In our case, it amounts to $O(P^2ZN)$. Multiplied by the complexity of the outer loop, it amounts to $O(P^3ZN)$ which is a lot when the number of partitions and nodes starts to be large. To avoid that, we adapt the Bellman-Ford algorithm.
+
+The Bellman-Ford algorithm runs $\#V$ iterations of an outer loop, and an inner loop over $E$. The idea is to compute the shortest paths from a source vertex $v$ to all other vertices. After $k$ iterations of the outer loop, the algorithm has computed all shortest path of length at most $k$. All simple paths have length at most $\#V-1$, so if there is an update in the last iteration of the loop, it means that there is a negative cycle in the graph. The observation that will enable us to improve the complexity is the following:
+
+\begin{proposition}
+	In the graph $G_f$ (and $G$), all simple paths have a length at most $4N$.
+\end{proposition}
+\begin{proof}
+	Since $f$ is a maximal flow, there is no outgoing edge from $\mathbf{s}$ in $G_f$. One can thus check than any simple path of length 4 must contain at least two node of type $\mathbf{n}$. Hence on a path, at most 4 arcs separate two successive nodes of type $\mathbf{n}$. 
+\end{proof}
+
+Thus, in the absence of negative cycles, shortest paths in $G_f$ have length at most $4N$. So we can do only $4N+1$ iterations of the outer loop in Bellman-Ford algorithm. This makes the complexity of the detection of one set of cycle to be $O(N\#E) = O(N^2 P)$.
+
+With this improvement, the complexity of the whole algorithm is, in the worst case, $O(N^2P^2)$. However, since we detect several cycles at once and we start with a flow that might be close to the previous one, the number of iterations of the outer loop might be smaller in practice.
+
+
+
+\subsubsection*{Metrics}
+We can display the node and zone utilization ratio, by dividing the flow passing through them divided by their outgoing capacity. In particular, we can pinpoint saturated nodes and zones (i.e. used at their full potential).
+
+We can display the distance to the previous assignment, and the number of partition transfers.
+
+
+
+
+
+\section{Properties of an optimal 3-strict assignment}
+
+\subsection{Optimal assignment}
+\label{sec:opt_assign}
+
+For every zone $z\in Z$, define the zone capacity $c_z = \sum_{v, z_v=z} c_v$ and define $C = \sum_v c_v = \sum_z c_z$.
+
+One can check that the best we could be doing to maximize $s^*$ would be to use the nodes proportionally to their capacity. This would yield $s^*=C/(3N)$. This is not possible because of (i) redundancy constraints and (ii) integer rounding but it gives and upper bound. 
+
+\subsubsection*{Optimal utilization}
+
+We call an \emph{utilization} a collection of non-negative integers $(n_v)_{v\in V}$ such that $\sum_v n_v = 3N$ and for every zone $z$, $\sum_{v\in z} n_v \le N$. We call such utilization \emph{optimal} if it maximizes $s^*$.
+
+We start by computing a node sub-utilization $(\hat{n}_v)_{v\in V}$ such that for every zone $z$, $\sum_{v\in z} \hat{n}_v \le N$ and we show that there is an optimal utilization respecting the constraints and such that $\hat{n}_v \le n_v$ for every node.
+
+Assume that there is a zone $z_0$ such that $c_{z_0}/C \ge 1/3$. Then for any $v\in z_0$, we define 
+$$\hat{n}_v = \left\lfloor\frac{c_v}{c_{z_0}}N\right\rfloor.$$ 
+This choice ensures for any such $v$ that
+$$
+\frac{c_v}{\hat{n}_v} \ge \frac{c_{z_0}}{N} \ge \frac{C}{3N}
+$$
+which is the universal upper bound on $s^*$. Hence any optimal utilization $(n_v)$ can be modified to another optimal utilization such that $n_v\ge \hat{n}_v$
+
+Because $z_0$ cannot store more than $N$ partition occurences, in any assignment, at least $2N$ partitions must be assignated to the zones $Z\setminus\{z_0\}$. Let $C_0 = C-c_{z_0}$. Suppose that there exists a zone $z_1\neq z_0$ such that $c_{z_1}/C_0 \ge 1/2$. Then, with the same argument as for $z_0$, we can define 
+$$\hat{n}_v = \left\lfloor\frac{c_v}{c_{z_1}}N\right\rfloor$$
+for every $v\in z_1$.
+
+Now we can assign the remaining partitions. Let $(\hat{N}, \hat{C})$ to be
+\begin{itemize}
+	\item $(3N,C)$ if we did not find any $z_0$;
+	\item $(2N,C-c_{z_0})$ if there was a $z_0$ but no $z_1$;
+	\item $(N,C-c_{z_0}-c_{z_1})$ if there was a $z_0$ and a $z_1$.
+\end{itemize}
+Then at least $\hat{N}$ partitions must be spread among the remaining zones. Hence $s^*$ is upper bounded by $\hat{C}/\hat{N}$ and without loss of generality, we can define, for every node that is not in $z_0$ nor $z_1$, 
+$$\hat{n}_v = \left\lfloor\frac{c_v}{\hat{C}}\hat{N}\right\rfloor.$$ 
+
+We constructed a sub-utilization $\hat{n}_v$. Now notice that $3N-\sum_v \hat{n}_v \le \# V$ where $\# V$ denotes the number of nodes. We can iteratively pick a node $v^*$ such that 
+\begin{itemize}
+	\item $\sum_{v\in z_{v^*}} \hat{n}_v < N$ where $z_{v^*}$ is the zone of $v^*$;
+	\item $v^*$ maximizes the quantity $c_v/(\hat{n}_v+1)$ among the vertices satisfying the first condition (i.e. not in a saturated zone).
+\end{itemize}
+We iterate these instructions until $\sum_v \hat{n}_v= 3N$, and at this stage we define $(n_v) = (\hat{n}_v)$. It is easy to prove by induction that at every step, there is an optimal utilization that is pointwise larger than $\hat{n}_v$, and in particular, that $(n_v)$ is optimal.
+
+\subsubsection*{Existence of an optimal assignment}
+
+As for now, the \emph{optimal utilization} that we obtained is just a vector of numbers and it is not clear that it can be realized as the utilization of some concrete assignment. Here is a way to get a concrete assignment.
+
+Define $3N$ tokens $t_1,\ldots, t_{3N}\in V$ as follows:
+\begin{itemize}
+	\item Enumerate the zones $z$ of $Z$ in any order;
+	\item enumerate the nodes $v$ of $z$ in any order;
+	\item repeat $n_v$ times the token $v$.
+\end{itemize} 
+Then for $1\le i \le N$, define the triplet $T_i$ to be 
+$(t_i, t_{i+N}, t_{i+2N})$. Since the same nodes of a zone appear contiguously, the three nodes of a triplet must belong to three distinct zones.
+
+However simple, this solution to go from an utilization to an assignment has the drawback of not spreading the triplets: a node will tend to be associated to the same two other nodes for many partitions. Hence, during data transfer, it will tend to use only two link, instead of spreading the bandwith use over many other links to other nodes. To achieve this goal, we will reframe the search of an assignment as a flow problem. and in the flow algorithm, we will introduce randomness in the order of exploration. This will be sufficient to obtain a good dispersion of the triplets.
+
+\begin{figure}
+	\centering
+	\includegraphics[width=0.9\linewidth]{figures/naive}
+	\caption{On the left, the creation of a concrete assignment with the naive approach of repeating tokens. On the right, the zones containing the nodes.}
+\end{figure}
+
+\subsubsection*{Assignment as a maximum flow problem}
+
+We describe the flow problem via its graph $(X,E)$ where $X$ is a set of vertices, and $E$ are directed weighted edges between the vertices. For every zone $z$, define $n_z=\sum_{v\in z} n_v$.
+
+The set of vertices $X$ contains the source $\mathbf{s}$ and the sink $\mathbf{t}$; a vertex $\mathbf{x}_z$ for every zone $z\in Z$, and a vertex $\mathbf{y}_i$ for every partition index $1\le i\le N$. 
+
+The set of edges $E$ contains
+\begin{itemize}
+	\item the edge $(\mathbf{s}, \mathbf{x}_z, n_z)$ for every zone $z\in Z$;
+	\item the edge $(\mathbf{x}_z, \mathbf{y}_i, 1)$ for every zone $z\in Z$ and partition $1\le i\le N$;
+	\item the edge $(\mathbf{y}_i, \mathbf{t}, 3)$ for every partition $1\le i\le N$.
+\end{itemize}
+
+\begin{figure}[b]
+	\centering
+	\includegraphics[width=0.6\linewidth]{figures/flow}
+	\caption{Flow problem to compute and optimal assignment.}
+\end{figure}
+
+We first show the equivalence between this problem and and the construction of an assignment. Given some optimal assignment $(n_v)$, define the flow $f:E\to \mathbb{N}$ that saturates every edge from $\mathbf{s}$ or to $\mathbf{t}$, takes value $1$ on the edge between $\mathbf{x}_z$ and $\mathbf{y}_i$ if partition $i$ is stored in some node of the zone $z$, and $0$ otherwise. One can easily check that $f$ thus defined is indeed a flow and is maximum.
+
+Reciprocally, by the existence of maximum flows constructed from optimal assignments, any maximum flow must saturate the edges linked to the source or the sink. It can only take value 0 or 1 on the other edge, and every partition vertex is associated to exactly three distinct zone vertices. Every zone is associated to exactly $n_z$ partitions.
+
+A maximum flow can be constructed using, for instance, Dinic's algorithm. This algorithm works by discovering augmenting path to iteratively increase the flow. During the exploration of the graph to find augmenting path, we can shuffle the order of enumeration of the neighbours to spread the associations between zones and partitions.
+
+Once we have such association, we can randomly distribute the $n_z$ edges picked for every zone $z$ to its nodes $v\in z$ such that every such $v$ gets $n_z$ edges. This defines an optimal assignment of partitions to nodes.
+
+
+\subsection{Minimal transfer}
+
+Assume that there was a previous assignment $(T'_i)_{1\le i\le N}$ corresponding to utilizations $(n'_v)_{v\in V}$. We would like the new computed assignment $(T_i)_{1\le i\le N}$ from some $(n_v)_{v\in V}$ to minimize the number of partitions that need to be transferred. We can imagine two different objectives corresponding to different hypotheses: 
+\begin{equation}
+	\tag{H3A}
+	\label{hyp:A}
+	\text{\emph{Transfers between different zones cost much more than inside a zone.}}
+\end{equation}
+\begin{equation}
+	\tag{H3B}
+	\label{hyp:B}
+	\text{\emph{Changing zone is not the largest cost when transferring a partition.}}
+\end{equation}
+
+In case $A$, our goal will be to minimize the number of changes of zone in the assignment of partitions to zone. More formally, we will maximize the quantity
+$$
+Q_Z := 
+\sum_{1\le i\le N} 
+\#\{z\in Z ~|~ z\cap T_i \neq \emptyset, z\cap T'_i \neq \emptyset \}
+.$$
+
+In case $B$, our goal will be to minimize the number of changes of nodes in the assignment of partitions to nodes. We will maximize the quantity
+$$
+Q_V :=
+\sum_{1\le i\le N} \#(T_i \cap T'_i).
+$$
+
+It is tempting to hope that there is a way to maximize both quantity, that having the least discrepancy in terms of nodes will lead to the least discrepancy in terms of zones. But this is actually wrong! We propose the following counter-example to convince the reader:
+
+We consider eight nodes $a, a', b, c, d, d', e, e'$ belonging to five different zones $\{a,a'\}, \{b\}, \{c\}, \{d,d'\}, \{e, e'\}$. We take three partitions ($N=3$), that are originally assigned with some utilization $(n'_v)_{v\in V}$ as follows:
+$$
+T'_1=(a,b,c) \qquad
+T'_2=(a',b,d) \qquad 
+T'_3=(b,c,e).
+$$
+This assignment, with updated utilizations $(n_v)_{v\in V}$ minimizes the number of zone changes:
+$$
+T_1=(d,b,c) \qquad
+T_2=(a,b,d) \qquad 
+T_3=(b,c,e').
+$$
+This one, with the same utilization, minimizes the number of node changes:
+$$
+T_1=(a,b,c) \qquad
+T_2=(e',b,d) \qquad 
+T_3=(b,c,d').
+$$
+One can check that in this case, it is impossible to minimize both the number of zone and node changes.
+
+Because of the redundancy constraint, we cannot use a greedy algorithm to just replace nodes in the triplets to try to get the new utilization rate: this could lead to blocking situation where there is still a hole to fill in a triplet but no available node satisfies the zone separation constraint. To circumvent this issue, we propose an algorithm based on finding cycles in a graph encoding of the assignment. As in section \ref{sec:opt_assign}, we can explore the neigbours in a random order in the graph algorithms, to spread the triplets distribution.
+
+
+\subsubsection{Minimizing the zone discrepancy}
+
+
+First, notice that, given an assignment of partitions to \emph{zones}, it is easy to deduce an assignment to \emph{nodes} that minimizes the number of transfers for this zone assignment: For every zone $z$ and every node $v\in z$, pick in any way a set $P_v$ of partitions that where assigned to $v$ in $T'$, to $z_v$ in $T$, with the cardinality of $P_v$ smaller than $n_v$. Once all these sets are chosen, complement the assignment to reach the right utilization for every node. If $\#P_v > n_v$, it means that all the partitions that could stay in $v$ (i.e. that were already in $v$ and are still assigned to its zone) do stay in $v$. If $\#P_v = n_v$, then $n_v$ partitions stay in $v$, which is the number of partitions that need to be in $v$ in the end. In both cases, we could not hope for better given the partition to zone assignment.
+
+Our goal now is to find a assignment of partitions to zones that minimizes the number of zone transfers. To do so we are going to represent an assignment as a graph.
+
+Let $G_T=(X,E_T)$ be the directed weighted graph with vertices $(\mathbf{x}_i)_{1\le i\le N}$ and $(\mathbf{y}_z)_{z\in Z}$. For any $1\le i\le N$ and $z\in Z$, $E_T$ contains  the arc:
+\begin{itemize}
+	\item $(\mathbf{x}_i, \mathbf{y}_z, +1)$, if $z$ appears in $T_i'$ and $T_i$;
+	\item $(\mathbf{x}_i, \mathbf{y}_z, -1)$, if $z$ appears in $T_i$ but not in $T'_i$;
+	\item $(\mathbf{y}_z, \mathbf{x}_i, -1)$, if $z$ appears in $T'_i$ but not in $T_i$;
+	\item $(\mathbf{y}_z, \mathbf{x}_i, +1)$, if $z$ does not appear in $T'_i$ nor in $T_i$.
+\end{itemize}
+In other words, the orientation of the arc encodes whether partition $i$ is stored in zone $z$ in the assignment $T$ and the weight $\pm 1$ encodes whether this corresponds to what happens in the assignment $T'$.
+
+\begin{figure}[t]
+	\centering
+	\begin{minipage}{.40\linewidth}
+		\centering
+		\includegraphics[width=.8\linewidth]{figures/mini_zone}
+	\end{minipage}
+	\begin{minipage}{.55\linewidth}
+		\centering
+		\includegraphics[width=.8\linewidth]{figures/mini_node}
+	\end{minipage}
+	\caption{On the left: the graph $G_T$ encoding an assignment to minimize the zone discrepancy. On the right: the graph $G_T$ encoding an assignment to minimize the node discrepancy.}
+\end{figure}
+
+
+Notice that at every partition, there are three outgoing arcs, and at every zone, there are $n_z$ incoming arcs. Moreover, if $w(e)$ is the weight of an arc $e$, define the weight of $G_T$ by
+\begin{align*}
+w(G_T) := \sum_{e\in E} w(e) &= \#Z \times N - 4 \sum_{1\le i\le N} \#\{z\in Z ~|~ z\cap T_i = \emptyset, z\cap T'_i \neq \emptyset\}	\\
+&=\#Z \times N - 4 \sum_{1\le i\le N} 3- \#\{z\in Z ~|~ z\cap T_i \neq \emptyset, z\cap T'_i \neq \emptyset\} \\
+&= (\#Z-12)N + 4 Q_Z.
+\end{align*}
+Hence maximizing $Q_Z$ is equivalent to maximizing $w(G_T)$.
+
+Assume that their exist some assignment $T^*$ with the same utilization $(n_v)_{v\in V}$. Define $G_{T^*}$ similarly and consider the set $E_\mathrm{Diff} = E_T \setminus E_{T^*}$ of arcs that appear only in $G_T$. Since all vertices have the same number of incoming arcs in $G_T$ and $G_{T^*}$, the vertices of the graph $(X, E_\mathrm{Diff})$ must all have the same number number of incoming and outgoing arrows. So $E_\mathrm{Diff}$ can be expressed as a union of disjoint cycles. Moreover, the edges of $E_\mathrm{Diff}$ must appear in $E_{T^*}$ with reversed orientation and opposite weight. Hence, we have
+$$
+ w(G_T) - w(G_{T^*}) = 2 \sum_{e\in E_\mathrm{Diff}} w(e). 
+$$
+Hence, if $T$ is not optimal, there exists some $T^*$ with $w(G_T) < w(G_{T^*})$, and by the considerations above, there must exist a cycle in $E_\mathrm{Diff}$, and hence in $G_T$, with negative weight. If we reverse the edges and weights along this cycle, we obtain some graph. Since we did not change the incoming degree of any vertex, this is the graph encoding of some valid assignment $T^+$ such that $w(G_{T^+}) > w(G_T)$. We can iterate this operation until there is no other assignment $T^*$ with larger weight, that is until we obtain an optimal assignment.
+
+
+
+\subsubsection{Minimizing the node discrepancy}
+
+We will follow an approach similar to the one where we minimize the zone discrepancy. Here we will directly obtain a node assignment from a graph encoding.
+
+Let $G_T=(X,E_T)$ be the directed weighted graph with vertices $(\mathbf{x}_i)_{1\le i\le N}$, $(\mathbf{y}_{z,i})_{z\in Z, 1\le i\le N}$ and $(\mathbf{u}_v)_{v\in V}$. For any $1\le i\le N$ and $z\in Z$, $E_T$ contains  the arc:
+\begin{itemize}
+	\item $(\mathbf{x}_i, \mathbf{y}_{z,i}, 0)$, if $z$ appears in $T_i$;
+	\item $(\mathbf{y}_{z,i}, \mathbf{x}_i, 0)$, if $z$ does not appear in $T_i$.
+\end{itemize}
+For any $1\le i\le N$ and $v\in V$, $E_T$ contains  the arc:
+\begin{itemize}
+	\item $(\mathbf{y}_{z_v,i}, \mathbf{u}_v, +1)$, if $v$ appears in $T_i'$ and $T_i$;
+	\item $(\mathbf{y}_{z_v,i}, \mathbf{u}_v, -1)$, if $v$ appears in $T_i$ but not in $T'_i$;
+	\item $(\mathbf{u}_v, \mathbf{y}_{z_v,i}, -1)$, if $v$ appears in $T'_i$ but not in $T_i$;
+	\item $(\mathbf{u}_v, \mathbf{y}_{z_v,i}, +1)$, if $v$ does not appear in $T'_i$ nor in $T_i$.
+\end{itemize}
+Every vertex $\mathbb{x}_i$ has outgoing degree 3, every vertex $\mathbf{y}_{z,v}$ has outgoing degree 1, and every vertex $\mathbf{u}_v$ has incoming degree $n_v$. 
+Remark that any graph respecting these degree constraints is the encoding of a valid assignment with utilizations $(n_v)_{v\in V}$, in particular no partition is stored in two nodes of the same zone.
+
+We define $w(G_T)$ similarly:
+\begin{align*}
+	w(G_T) := \sum_{e\in E_T} w(e) &= \#V \times N - 4\sum_{1\le i\le N} 3-\#(T_i\cap T'_i) \\
+	&= (\#V-12)N + 4Q_V.
+\end{align*}
+
+Exactly like in the previous section, the existence of an assignment with larger weight implies the existence of a negatively weighted cycle in $G_T$. Reversing this cycle gives us the encoding of a valid assignment with a larger weight. Iterating this operation yields an optimal assignment.
+
+
+\subsubsection{Linear combination of both criteria}
+
+In the graph $G_T$ defined in the previous section, instead of having weights $0$ and $\pm 1$, we could be having weights $\pm\alpha$ between $\mathbf{x}$ and  $\mathbf{y}$ vertices, and weights $\pm\beta$ between $\mathbf{y}$ and  $\mathbf{u}$ vertices, for some $\alpha,\beta>0$ (we have positive weight if the assignment corresponds to $T'$ and negative otherwise). Then
+\begin{align*}
+	w(G_T) &= \sum_{e\in E_T} w(e) = 
+	\alpha \big( (\#Z-12)N + 4 Q_Z\big) + 
+	\beta \big( (\#V-12)N + 4 Q_V\big) \\
+	&= \mathrm{const}+ 4(\alpha Q_Z + \beta Q_V).
+\end{align*}
+So maximizing the weight of such graph encoding would be equivalent to maximizing a linear combination of $Q_Z$ and $Q_V$.
+
+
+\subsection{Algorithm}
+We give a high level description of the algorithm to compute an optimal 3-strict assignment. The operations appearing at lines 1,2,4 are respectively described by Algorithms \ref{alg:util},\ref{alg:opt} and \ref{alg:mini}.
+
+
+
+\begin{algorithm}[H]
+	\caption{Optimal 3-strict assignment}
+	\label{alg:total}
+	\begin{algorithmic}[1]
+	\Function{Optimal 3-strict assignment}{$N$, $(c_v)_{v\in V}$, $T'$}
+		\State $(n_v)_{v\in V} \leftarrow$ \Call{Compute optimal utilization}{$N$, $(c_v)_{v\in V}$}
+		\State $(T_i)_{1\le i\le N} \leftarrow$ \Call{Compute candidate assignment}{$N$, $(n_v)_{v\in V}$}
+		\If {there was a previous assignment $T'$}
+			\State $T \leftarrow$ \Call{Minimization of transfers}{$(T_i)_{1\le i\le N}$, $(T'_i)_{1\le i\le N}$}
+		\EndIf
+		\State \Return $T$.
+	\EndFunction
+	\end{algorithmic}
+\end{algorithm}
+
+We give some considerations of worst case complexity for these algorithms. In the following, we assume $N>\#V>\#Z$. The complexity of Algorithm \ref{alg:total} is $O(N^3\# Z)$ if we assume \eqref{hyp:A} and $O(N^3 \#Z \#V)$ if we assume \eqref{hyp:B}.
+
+Algorithm \ref{alg:util} can be implemented with complexity $O(\#V^2)$. The complexity of the function call at line \ref{lin:subutil} is $O(\#V)$. The difference between the sum of the subutilizations and $3N$ is at most the sum of the rounding errors when computing the $\hat{n}_v$. Hence it is bounded by $\#V$ and the loop at line \ref{lin:loopsub} is iterated at most $\#V$ times. Finding the minimizing $v$ at line \ref{lin:findmin} takes $O(\#V)$ operations (naively, we could also use a heap).
+
+Algorithm \ref{alg:opt} can be implemented with complexity $O(N^3\times \#Z)$. The flow graph has $O(N+\#Z)$ vertices and $O(N\times \#Z)$ edges. Dinic's algorithm has complexity $O(\#\mathrm{Vertices}^2\#\mathrm{Edges})$ hence in our case it is $O(N^3\times \#Z)$.
+ 
+Algorithm \ref{alg:mini} can be implented with complexity $O(N^3\# Z)$ under \eqref{hyp:A} and $O(N^3 \#Z \#V)$ under \eqref{hyp:B}.
+The graph $G_T$ has $O(N)$ vertices and $O(N\times \#Z)$ edges under assumption \eqref{hyp:A} and respectively $O(N\times \#Z)$ vertices and $O(N\times \#V)$ edges under assumption \eqref{hyp:B}. The loop at line \ref{lin:repeat} is iterated at most $N$ times since the distance between $T$ and $T'$ decreases at every iteration. Bellman-Ford algorithm has complexity $O(\#\mathrm{Vertices}\#\mathrm{Edges})$, which in our case amounts to $O(N^2\# Z)$ under \eqref{hyp:A} and $O(N^2 \#Z \#V)$ under \eqref{hyp:B}.
+ 
+\begin{algorithm}
+	\caption{Computation of the optimal utilization}
+	\label{alg:util}
+	\begin{algorithmic}[1]
+\Function{Compute optimal utilization}{$N$, $(c_v)_{v\in V}$}
+	\State $(\hat{n}_v)_{v\in V} \leftarrow $ \Call{Compute subutilization}{$N$, $(c_v)_{v\in V}$} \label{lin:subutil}
+	\While{$\sum_{v\in V} \hat{n}_v < 3N$} \label{lin:loopsub}
+	\State Pick $v\in V$ minimizing $\frac{c_v}{\hat{n}_v+1}$ and such that
+		$\sum_{v'\in z_v} \hat{n}_{v'} < N$ \label{lin:findmin}
+		\State $\hat{n}_v \leftarrow \hat{n}_v+1$
+	\EndWhile
+	\State \Return $(\hat{n}_v)_{v\in V}$
+\EndFunction
+\State
+
+\Function{Compute subutilization}{$N$, $(c_v)_{v\in V}$}
+		\State $R \leftarrow 3$
+\For{$v\in V$}
+\State $\hat{n}_v \leftarrow \mathrm{unset}$
+\EndFor
+\For{$z\in Z$}
+\State $c_z \leftarrow \sum_{v\in z} c_v$
+\EndFor
+\State $C \leftarrow \sum_{z\in Z} c_z$
+\While{$\exists z \in Z$ such that $R\times c_{z} > C$}
+\For{$v\in z$}
+\State $\hat{n}_v \leftarrow \left\lfloor \frac{c_v}{c_z} N \right\rfloor$
+\EndFor
+\State $C \leftarrow C-c_z$
+\State $R\leftarrow R-1$
+\EndWhile
+\For{$v\in V$}
+\If{$\hat{n}_v = \mathrm{unset}$}
+\State $\hat{n}_v \leftarrow \left\lfloor \frac{Rc_v}{C} N \right\rfloor$
+\EndIf
+\EndFor
+\State \Return $(\hat{n}_v)_{v\in V}$
+\EndFunction
+	\end{algorithmic}
+\end{algorithm}
+
+\begin{algorithm}
+	\caption{Computation of a candidate assignment}
+	\label{alg:opt}
+	\begin{algorithmic}[1]
+		\Function{Compute candidate assignment}{$N$, $(n_v)_{v\in V}$}
+		\State Compute the flow graph $G$
+		\State Compute the maximal flow $f$ using Dinic's algorithm with randomized neighbours enumeration
+		\State Construct the assignment $(T_i)_{1\le i\le N}$ from $f$
+		\State \Return $(T_i)_{1\le i\le N}$
+		\EndFunction
+	\end{algorithmic}
+\end{algorithm}
+
+
+\begin{algorithm}
+	\caption{Minimization of the number of transfers}
+	\label{alg:mini}
+	\begin{algorithmic}[1]
+		\Function{Minimization of transfers}{$(T_i)_{1\le i\le N}$, $(T'_i)_{1\le i\le N}$}
+		\State Construct the graph encoding $G_T$
+		\Repeat \label{lin:repeat}
+		\State Find a negative cycle $\gamma$ using Bellman-Ford algorithm on $G_T$
+		\State Reverse the orientations and weights of edges in $\gamma$
+		\Until{no negative cycle is found}
+		\State Update $(T_i)_{1\le i\le N}$ from $G_T$
+		\State \Return $(T_i)_{1\le i\le N}$
+		\EndFunction
+	\end{algorithmic}
+\end{algorithm}
+
+\newpage
+
+\section{Computation of a 3-non-strict assignment}
+
+\subsection{Choices of optimality}
+
+In this mode, we primarily want to store every partition on three nodes, and only secondarily try to spread the nodes among different zone. So we make the choice of not taking the zone repartition in the criterion of optimality.
+
+We try to maximize $s^*$ defined in \eqref{eq:optimal}. So we can compute the optimal utilizations $(n_v)_{v\in V}$ with the only constraint that $n_v \le N$ for every node $v$. As in the previous section, we start with a sub-utilization proportional to $c_v$ (and capped at $N$), and we iteratively increase the $\hat{n}_v$ that is less than $N$ and maximizes the quantity $c_v/(\hat{n}_v+1)$, until the total sum is $3N$.
+
+\subsection{Computation of a candidate assignment}
+
+To compute a candidate assignment (that does not optimize zone spreading nor distance to a previous assignment yet), we can use the folowing flow problem.
+
+Define the oriented weighted graph $(X,E)$. The set of vertices $X$ contains the source $\mathbf{s}$, the sink $\mathbf{t}$, vertices 
+$\mathbf{x}_p, \mathbf{u}^+_p, \mathbf{u}^-_p$ for every partition $p$, vertices $\mathbf{y}_{p,z}$ for every partition $p$ and zone $z$, and vertices $\mathbf{z}_v$ for every node $v$. 
+
+The set of edges is composed of the following arcs:
+\begin{itemize}
+	\item ($\mathbf{s}$,$\mathbf{x}_p$, 3) for every partition $p$;
+	\item ($\mathbf{x}_p$,$\mathbf{u}^+_p$, 3) for every partition $p$;
+	\item ($\mathbf{x}_p$,$\mathbf{u}^-_p$, 2) for every partition $p$;
+	\item ($\mathbf{u}^+_p$,$\mathbf{y}_{p,z}$, 1) for every partition $p$ and zone $z$;
+	\item ($\mathbf{u}^-_p$,$\mathbf{y}_{p,z}$, 2) for every partition $p$ and zone $z$;
+	\item ($\mathbf{y}_{p,z}$,$\mathbf{z}_v$, 1) for every partition $p$, zone $z$ and node $v\in z$;
+	\item ($\mathbf{z}_v$, $\mathbf{t}$, $n_v$) for every node $v$;
+\end{itemize}
+
+One can check that any maximal flow in this graph corresponds to an assignment of partitions to nodes. In such a flow, all the arcs from $\mathbf{s}$ and to $\mathbf{t}$ are saturated. The arc from $\mathbf{y}_{p,z}$ to $\mathbf{z}_v$ is saturated if and only if $p$ is associated to~$v$. 
+Finally the flow from $\mathbf{x}_p$ to $\mathbf{y}_{p,z}$ can go either through $\mathbf{u}^+_p$ or $\mathbf{u}^-_p$.
+
+
+
+\subsection{Maximal spread and minimal transfers}
+Notice that if the arc $\mathbf{u}_p^+\mathbf{y}_{p,z}$ is not saturated but there is some flow in $\mathbf{u}_p^-\mathbf{y}_{p,z}$, then it is possible to transfer a unit of flow from the path  $\mathbf{x}_p\mathbf{u}_p^-\mathbf{y}_{p,z}$ to the path $\mathbf{x}_p\mathbf{u}_p^+\mathbf{y}_{p,z}$. So we can always find an equivalent maximal flow $f^*$ that uses the path through $\mathbf{u}_p^-$ only if the path through $\mathbf{u}_p^+$ is saturated.
+
+We will use this fact to consider the amount of flow going through the vertices $\mathbf{u}^+$ as a measure of how well the partitions are spread over nodes belonging to different zones. If the partition $p$ is associated to 3 different zones, then a flow of 3 will cross $\mathbf{u}_p^+$ in $f^*$ (i.e. a flow of 0 will cross $\mathbf{u}_p^+$). If $p$ is associated to two zones, a flow of $2$ will cross $\mathbf{u}_p^+$. If $p$ is associated to a single zone, a flow of $1$ will cross $\mathbf{u}_p^+$.
+
+Let $N_1, N_2, N_3$ be the number of partitions associated to respectively 1,2 and 3 distinct zones. We will optimize a linear combination of these variables using the discovery of positively weighted circuits in a graph.
+
+At the same step, we will also optimize the distance to a previous assignment $T'$. Let $\alpha> \beta> \gamma \ge 0$ be three parameters.
+
+Given the flow $f$, let $G_f=(X',E_f)$ be the multi-graph where $X' = X\setminus\{\mathbf{s},\mathbf{t}\}$. The set $E_f$ is composed of the arcs:
+\begin{itemize}
+\item As many arcs from $(\mathbf{x}_p, \mathbf{u}^+_p,\alpha), (\mathbf{x}_p, \mathbf{u}^+_p,\beta), (\mathbf{x}_p, \mathbf{u}^+_p,\gamma)$ (selected in this order) as there is flow crossing $\mathbf{u}^+_p$ in $f$;
+\item As many arcs from $(\mathbf{u}^+_p, \mathbf{x}_p,-\gamma), (\mathbf{u}^+_p, \mathbf{x}_p,-\beta), (\mathbf{u}^+_p, \mathbf{x}_p,-\alpha)$ (selected in this order) as there is flow crossing $\mathbf{u}^-_p$ in $f$;
+\item  As many copies of $(\mathbf{x}_p, \mathbf{u}^-_p,0)$ as there is flow through $\mathbf{u}^-_p$;
+\item  As many copies of $(\mathbf{u}^-_p,\mathbf{x}_p,0)$ so that the number of arcs between these two vertices is 2;
+\item $(\mathbf{u}^+_p,\mathbf{y}_{p,z}, 0)$ if the flow between these vertices is 1, and the opposite arc otherwise;
+\item as many copies of $(\mathbf{u}^-_p,\mathbf{y}_{p,z}, 0)$ as the flow between these vertices, and as many copies of the opposite arc as 2~$-$~the flow;
+\item $(\mathbf{y}_{p,z},\mathbf{z}_v, \pm1)$ if it is saturated in $f$, with $+1$ if $v\in T'_p$ and $-1$ otherwise;
+\item $(\mathbf{z}_v,\mathbf{y}_{p,z}, \pm1)$ if it is not saturated in $f$, with $+1$ if $v\notin T'_p$ and $-1$ otherwise.
+\end{itemize}
+To summarize, arcs are oriented left to right if they correspond to a presence of flow in $f$, and right to left if they correspond to an absence of flow. They are positively weighted if we want them to stay at their current state, and negatively if we want them to switch. Let us compute the weight of such graph.
+
+\begin{multline*}
+	w(G_f)  = \sum_{e\in E_f} w(e_f)  \\
+	= 
+	(\alpha - \beta -\gamma) N_1 + (\alpha +\beta - \gamma) N_2 + (\alpha+\beta+\gamma) N_3 
+	\\ + 
+	\#V\times N - 4 \sum_p 3-\#(T_p\cap T'_p) \\ 
+	=(\#V-12+\alpha-\beta-\gamma)\times N + 4Q_V + 2\beta N_2 + 2(\beta+\gamma) N_3 \\
+\end{multline*}
+
+As for the mode 3-strict, one can check that the difference of two such graphs corresponding to the same $(n_v)$ is always eulerian. Hence we can navigate in this class with the same greedy algorithm that discovers positive cycles and flips them.
+
+The function that we optimize is 
+$$
+2Q_V +  \beta N_2 + (\beta+\gamma) N_3.
+$$
+The choice of parameters $\beta$ and $\gamma$ should be lead by the following question: For $\beta$, where to put the tradeoff between zone dispersion and distance to the previous configuration? For $\gamma$, do we prefer to have more partitions spread between 2 zones, or have less between at least 2 zones but more between 3 zones.
+
+The quantity $Q_V$ varies between $0$ and $3N$, it should be of order $N$. The quantity $N_2+N_3$ should also be of order $N$ (it is exactly $N$ in the strict mode). So the two terms of the function are comparable. 
+
+
+\bibliography{optimal_layout} 
+\bibliographystyle{ieeetr}
+
+\end{document}
+
+
+
@@ -1 +0,0 @@
-.direnv/
@@ -1,17 +0,0 @@
-*
-
-!*.txt
-!*.md
-
-!assets
-
-!.gitignore
-!*.svg
-!*.png
-!*.jpg
-!*.tex
-!Makefile
-!.gitignore
-!assets/*.drawio.pdf
-
-!talk.pdf
@@ -1,34 +0,0 @@
-ASSETS=assets/consistent_hashing_1.pdf \
-	   assets/consistent_hashing_2.pdf \
-	   assets/consistent_hashing_3.pdf \
-	   assets/consistent_hashing_4.pdf \
-	   assets/garage_tables.pdf \
-	   assets/consensus.pdf_tex \
-	   assets/lattice1.pdf_tex \
-	   assets/lattice2.pdf_tex \
-	   assets/lattice3.pdf_tex \
-	   assets/lattice4.pdf_tex \
-	   assets/lattice5.pdf_tex \
-	   assets/lattice6.pdf_tex \
-	   assets/lattice7.pdf_tex \
-	   assets/lattice8.pdf_tex \
-	   assets/latticeB_1.pdf_tex \
-	   assets/latticeB_2.pdf_tex \
-	   assets/latticeB_3.pdf_tex \
-	   assets/latticeB_4.pdf_tex \
-	   assets/latticeB_5.pdf_tex \
-	   assets/latticeB_6.pdf_tex \
-	   assets/latticeB_7.pdf_tex \
-	   assets/latticeB_8.pdf_tex \
-	   assets/latticeB_9.pdf_tex \
-	   assets/latticeB_10.pdf_tex \
-	   assets/deuxfleurs.pdf
-
-talk.pdf: talk.tex $(ASSETS)
-	pdflatex talk.tex
-
-assets/%.pdf: assets/%.svg
-	inkscape -D -z --file=$^ --export-pdf=$@
-
-assets/%.pdf_tex: assets/%.svg
-	inkscape -D -z --file=$^ --export-pdf=$@ --export-latex
@@ -1,39 +0,0 @@
-### (fr) Garage, un système de stockage de données géo-distribué léger et robuste
-
-Garage est un système de stockage de données léger, géo-distribué, qui
-implémente le protocole de stockage S3 de Amazon. Garage est destiné
-principalement à l'auto-hébergement sur du matériel courant d'occasion. À ce
-titre, il doit tolérer un grand nombre de pannes: coupures de courant, coupures
-de connexion Internet, pannes de machines, ... Il doit également être facile à
-déployer et à maintenir, afin de pouvoir être facilement utilisé par des
-amateurs ou des petites organisations.
-
-Cette présentation vous proposera un aperçu de Garage et du choix technique
-principal qui rend un système comme Garage possible: le refus d'utiliser des
-algorithmes de consensus, remplacés avantageusement par des méthodes à
-cohérence faible.  Notre modèle est fortement inspiré de la base de donnée
-Dynamo (DeCandia et al, 2007), et fait usage des types de données CRDT (Shapiro
-et al, 2011).  Nous exploreront comment ces méthodes s'appliquent à la
-construction de l'abstraction "stockage objet" dans un système distribué, et
-quelles autres abstractions peuvent ou ne peuvent pas être construites dans ce
-modèle.
-
-### (en) Garage, a lightweight and robust geo-distributed data storage system
-
-Garage is a lightweight geo-distributed data store that implements the Amazon
-S3 object storage protocol.  Garage is meant primarily for self-hosting at home
-on second-hand commodity hardware, meaning it has to tolerate a wide variety of
-failure scenarios such as power cuts, Internet disconnections and machine
-crashes. It also has to be easy to deploy and maintain, so that hobbyists and
-small organizations can use it without trouble. 
-
-This talk will present Garage and the key technical choice that made Garage
-possible: refusing to use consensus algorithms and using instead weak
-consistency methods, with a model that is loosely based on that of the Dynamo
-database (DeCandia et al, 2007) and that makes heavy use of conflict-free
-replicated data types (Shapiro et al, 2011).  We will explore how these methods
-are suited to building the "object store" abstraction in a distributed system,
-and what other abstractions are possible or impossible to build in this model.
-
-
-
@@ -1,137 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="800"
-   height="300"
-   viewBox="0 0 211.66666 79.374999"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="consensus.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.4734708"
-     inkscape:cx="310.49139"
-     inkscape:cy="179.1688"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer1" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1">
-    <g
-       id="g1218"
-       transform="translate(-8.9161476,-12.502301)">
-      <circle
-         style="fill:#ffffff;stroke:#000000;stroke-width:1;stroke-dasharray:none;stroke-opacity:1"
-         id="path111"
-         cx="38.904896"
-         cy="37.936272"
-         r="13.474442" />
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="38.879501"
-         y="40.908073"
-         id="text1105"><tspan
-           sodipodi:role="line"
-           id="tspan1103"
-           style="stroke-width:0.264583;fill:#000000"
-           x="38.879501"
-           y="40.908073">$\bot$</tspan></text>
-    </g>
-    <g
-       id="g1218-3"
-       transform="translate(127.41938,-12.502301)">
-      <circle
-         style="fill:#ffffff;stroke:#000000;stroke-width:1;stroke-dasharray:none;stroke-opacity:1"
-         id="path111-5"
-         cx="38.904896"
-         cy="37.936272"
-         r="13.474442" />
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="38.879501"
-         y="40.908073"
-         id="text1105-6"><tspan
-           sodipodi:role="line"
-           id="tspan1103-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="38.879501"
-           y="40.908073">$x$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 44.289635,25.433971 H 145.90576"
-       id="path1414"
-       sodipodi:nodetypes="cc" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="92.729836"
-       y="21.781803"
-       id="text2092"><tspan
-         sodipodi:role="line"
-         id="tspan2090"
-         style="stroke-width:0.264583;fill:#000000"
-         x="92.729836"
-         y="21.781803">$propose(x) / x$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="166.29887"
-       y="69.89299"
-       id="text2092-9"><tspan
-         sodipodi:role="line"
-         id="tspan2090-1"
-         style="stroke-width:0.264583;fill:#000000"
-         x="166.29887"
-         y="69.89299">$propose(y) / x$</tspan></text>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="m 155.82329,35.899857 c -8.35129,12.319651 0.54055,24.640898 11.72797,24.072085 8.65403,-0.440005 18.59818,-11.705963 11.8146,-20.570891"
-       id="path2150"
-       sodipodi:nodetypes="csc" />
-  </g>
-</svg>
@@ -1,91 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<svg
-   viewBox="0 0 70.424515 70.300102"
-   version="1.1"
-   id="svg8"
-   sodipodi:docname="logo.svg"
-   inkscape:version="1.1 (c68e22c387, 2021-05-23)"
-   inkscape:export-filename="/home/quentin/Documents/dev/deuxfleurs/site/src/img/logo.png"
-   inkscape:export-xdpi="699.30194"
-   inkscape:export-ydpi="699.30194"
-   width="70.424515"
-   height="70.300102"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <defs
-     id="defs12" />
-  <sodipodi:namedview
-     id="namedview10"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:pageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     showgrid="false"
-     inkscape:zoom="12.125"
-     inkscape:cx="43.092783"
-     inkscape:cy="48.082474"
-     inkscape:window-width="3072"
-     inkscape:window-height="1659"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="svg8" />
-  <g
-     id="g79969"
-     transform="translate(-0.827,34.992103)">
-    <path
-       fill="#ffffff"
-       d="m 15.632,34.661 c -0.799,-0.597 -1.498,-1.484 -2.035,-2.592 l -0.228,-0.47 -0.46,0.249 c -0.975,0.528 -1.913,0.858 -2.744,0.969 L 9.963,29.061 6.327,30.029 C 6.17,29.175 6.202,28.142 6.423,27.007 L 6.526,26.482 5.994,26.416 C 4.752,26.262 3.688,25.891 2.89,25.336 L 4.411,22.419 1.423,20.896 C 1.742,19.952 2.371,19.014 3.257,18.161 L 3.634,17.798 3.255,17.438 C 2.452,16.674 1.847,15.884 1.485,15.127 L 4.995,13.774 2.95,10.615 C 3.69,10.213 4.643,9.929 5.739,9.783 L 6.258,9.715 6.167,9.201 C 5.952,7.99 5.995,6.863 6.291,5.913 l 3.308,0.523 0.524,-3.308 c 0.988,0.013 2.08,0.326 3.164,0.907 L 13.749,4.283 13.975,3.81 C 14.454,2.807 15.019,1.986 15.628,1.406 L 18,4.326 20.372,1.406 c 0.609,0.58 1.175,1.401 1.653,2.404 l 0.226,0.473 0.462,-0.247 C 23.798,3.455 24.891,3.142 25.877,3.13 L 26.4,6.438 29.71,5.913 c 0.296,0.951 0.34,2.078 0.124,3.288 l -0.092,0.515 0.518,0.069 c 1.095,0.145 2.048,0.43 2.788,0.832 l -2.046,3.156 3.511,1.355 c -0.361,0.757 -0.966,1.547 -1.77,2.311 l -0.379,0.36 0.377,0.363 c 0.888,0.854 1.516,1.793 1.835,2.736 l -2.984,1.52 1.521,2.984 c -0.812,0.574 -1.871,0.964 -3.094,1.134 l -0.518,0.072 0.096,0.514 c 0.201,1.089 0.226,2.083 0.073,2.909 l -3.634,-0.97 -0.204,3.757 c -0.83,-0.11 -1.768,-0.44 -2.742,-0.968 l -0.459,-0.249 -0.228,0.47 c -0.539,1.107 -1.237,1.994 -2.036,2.591 L 18,32.293 Z"
-       id="path2" />
-    <path
-       d="M 7.092,10.678 C 6.562,9.189 6.394,7.708 6.66,6.478 l 2.368,0.375 0.987,0.156 0.157,-0.988 0.375,-2.368 C 11.808,3.78 13.16,4.396 14.409,5.359 14.527,5.022 14.653,4.696 14.791,4.392 13.24,3.257 11.568,2.629 10.061,2.629 9.938,2.629 9.816,2.633 9.695,2.642 L 9.184,5.865 5.96,5.354 C 5.36,6.841 5.395,8.769 6.045,10.747 6.38,10.71 6.729,10.686 7.092,10.678 Z M 21.593,5.359 c 1.248,-0.962 2.6,-1.578 3.86,-1.705 l 0.376,2.368 0.156,0.988 0.987,-0.157 2.369,-0.376 c 0.266,1.23 0.098,2.71 -0.432,4.2 0.361,0.009 0.711,0.032 1.046,0.07 C 30.606,8.769 30.64,6.841 30.04,5.353 L 26.815,5.865 26.304,2.641 c -0.12,-0.008 -0.242,-0.012 -0.365,-0.012 -1.507,0 -3.179,0.628 -4.73,1.762 0.14,0.306 0.266,0.631 0.384,0.968 z M 7.368,27 h 0.035 c 0.067,0 0.157,-0.604 0.26,-0.947 -0.098,0.004 -0.197,0.046 -0.294,0.046 -1.496,0 -2.826,-0.303 -3.83,-0.89 L 4.628,23.081 5.082,22.194 4.191,21.742 2.055,20.654 C 2.563,19.503 3.57,18.404 4.873,17.511 4.586,17.292 4.312,17.07 4.063,16.842 2.376,18.059 1.217,19.597 0.828,21.152 l 2.908,1.483 -1.482,2.843 C 3.475,26.501 5.303,27 7.368,27 Z m 27.806,-5.846 c -0.39,-1.555 -1.548,-3.093 -3.234,-4.311 -0.25,0.228 -0.523,0.451 -0.81,0.669 1.304,0.893 2.31,1.992 2.817,3.145 l -2.136,1.088 -0.891,0.453 0.454,0.892 1.089,2.137 c -1.004,0.587 -2.332,0.904 -3.828,0.904 -0.099,0 -0.199,-0.01 -0.299,-0.013 0.103,0.344 0.192,0.683 0.26,1.011 l 0.039,0.002 c 2.066,0 3.892,-0.563 5.112,-1.587 l -1.482,-2.908 z m -12.653,9.182 c -0.447,1.517 -1.181,2.812 -2.119,3.651 L 18.707,32.293 18,31.586 l -0.707,0.707 -1.695,1.694 c -0.938,-0.839 -1.673,-2.136 -2.12,-3.652 -0.296,0.206 -0.593,0.397 -0.886,0.563 0.636,1.98 1.741,3.559 3.1,4.409 L 18,33 l 2.308,2.308 c 1.358,-0.851 2.464,-2.428 3.101,-4.408 -0.295,-0.168 -0.591,-0.359 -0.888,-0.564 z"
-       fill="#ea596e"
-       id="path4" />
-    <path
-       fill="#ea596e"
-       d="m 20.118,5.683 c 0.426,1.146 0.748,2.596 0.841,4.284 l 0.2,3.683 3.564,-0.946 c 1.32,-0.351 2.655,-0.536 3.86,-0.536 0.16,0 0.318,0.003 0.474,0.01 l -1.827,2.819 3.139,1.211 c -0.958,0.759 -2.237,1.514 -3.814,2.123 l -3.441,1.328 2.001,3.099 c 0.918,1.42 1.509,2.782 1.838,3.96 L 23.709,25.853 23.527,29.21 C 22.508,28.533 21.395,27.55 20.329,26.237 L 18,23.374 15.672,26.236 c -1.066,1.312 -2.179,2.295 -3.198,2.972 l -0.18,-3.354 -3.248,0.864 c 0.329,-1.178 0.921,-2.54 1.839,-3.961 L 12.889,19.658 9.447,18.33 C 7.87,17.721 6.591,16.967 5.633,16.208 L 8.768,15 6.941,12.177 c 0.155,-0.006 0.313,-0.01 0.473,-0.01 1.206,0 2.541,0.185 3.861,0.536 l 3.564,0.947 0.202,-3.683 c 0.092,-1.688 0.415,-3.138 0.84,-4.284 L 18,8.292 20.118,5.683 M 20.308,0.692 18,3.533 15.692,0.692 C 13.703,2.224 12.271,5.684 12.046,9.804 10.429,9.374 8.854,9.167 7.414,9.167 c -2.11,0 -3.929,0.445 -5.161,1.289 l 1.989,3.073 -3.415,1.316 c 0.842,2.366 3.69,4.797 7.54,6.283 -2.241,3.465 -3.116,7.106 -2.407,9.516 l 3.537,-0.941 0.196,3.654 c 2.512,-0.07 5.703,-2.027 8.307,-5.228 2.603,3.201 5.796,5.158 8.306,5.228 l 0.198,-3.655 3.535,0.943 c 0.71,-2.411 -0.165,-6.05 -2.404,-9.517 3.849,-1.485 6.696,-3.918 7.538,-6.283 l -3.415,-1.318 1.99,-3.07 c -1.233,-0.844 -3.053,-1.29 -5.164,-1.29 -1.438,0 -3.013,0.207 -4.63,0.636 C 23.729,5.684 22.297,2.224 20.308,0.692 Z"
-       id="path6" />
-  </g>
-  <g
-     id="g79964"
-     transform="translate(-1.043816,35.993714)">
-    <path
-       fill="#ffffff"
-       d="m 51.92633,-2.0247139 c -0.799,-0.597 -1.498,-1.484 -2.035,-2.592 l -0.228,-0.47 -0.46,0.249 c -0.975,0.528 -1.913,0.858 -2.744,0.969 l -0.202,-3.7560001 -3.636,0.968 c -0.157,-0.854 -0.125,-1.887 0.096,-3.022 l 0.103,-0.525 -0.532,-0.066 c -1.242,-0.154 -2.306,-0.525 -3.104,-1.08 l 1.521,-2.917 -2.988,-1.523 c 0.319,-0.944 0.948,-1.882 1.834,-2.735 l 0.377,-0.363 -0.379,-0.36 c -0.803,-0.764 -1.408,-1.554 -1.77,-2.311 l 3.51,-1.353 -2.045,-3.159 c 0.74,-0.402 1.693,-0.686 2.789,-0.832 l 0.519,-0.068 -0.091,-0.514 c -0.215,-1.211 -0.172,-2.338 0.124,-3.288 l 3.308,0.523 0.524,-3.308 c 0.988,0.013 2.08,0.326 3.164,0.907 l 0.462,0.248 0.226,-0.473 c 0.479,-1.003 1.044,-1.824 1.653,-2.404 l 2.372,2.92 2.372,-2.92 c 0.609,0.58 1.175,1.401 1.653,2.404 l 0.226,0.473 0.462,-0.247 c 1.085,-0.581 2.178,-0.894 3.164,-0.906 l 0.523,3.308 3.31,-0.525 c 0.296,0.951 0.34,2.078 0.124,3.288 l -0.092,0.515 0.518,0.069 c 1.095,0.145 2.048,0.43 2.788,0.832 l -2.046,3.156 3.511,1.355 c -0.361,0.757 -0.966,1.547 -1.77,2.311 l -0.379,0.36 0.377,0.363 c 0.888,0.854 1.516,1.793 1.835,2.736 l -2.984,1.52 1.521,2.984 c -0.812,0.574 -1.871,0.964 -3.094,1.134 l -0.518,0.072 0.096,0.514 c 0.201,1.089 0.226,2.083 0.073,2.909 l -3.634,-0.97 -0.204,3.7570001 c -0.83,-0.11 -1.768,-0.44 -2.742,-0.968 l -0.459,-0.249 -0.228,0.47 c -0.539,1.107 -1.237,1.994 -2.036,2.591 l -2.367,-2.369 z"
-       id="path2-9" />
-    <path
-       d="m 43.38633,-26.007714 c -0.53,-1.489 -0.698,-2.97 -0.432,-4.2 l 2.368,0.375 0.987,0.156 0.157,-0.988 0.375,-2.368 c 1.261,0.127 2.613,0.743 3.862,1.706 0.118,-0.337 0.244,-0.663 0.382,-0.967 -1.551,-1.135 -3.223,-1.763 -4.73,-1.763 -0.123,0 -0.245,0.004 -0.366,0.013 l -0.511,3.223 -3.224,-0.511 c -0.6,1.487 -0.565,3.415 0.085,5.393 0.335,-0.037 0.684,-0.061 1.047,-0.069 z m 14.501,-5.319 c 1.248,-0.962 2.6,-1.578 3.86,-1.705 l 0.376,2.368 0.156,0.988 0.987,-0.157 2.369,-0.376 c 0.266,1.23 0.098,2.71 -0.432,4.2 0.361,0.009 0.711,0.032 1.046,0.07 0.651,-1.978 0.685,-3.906 0.085,-5.394 l -3.225,0.512 -0.511,-3.224 c -0.12,-0.008 -0.242,-0.012 -0.365,-0.012 -1.507,0 -3.179,0.628 -4.73,1.762 0.14,0.306 0.266,0.631 0.384,0.968 z m -14.225,21.641 h 0.035 c 0.067,0 0.157,-0.604 0.26,-0.947 -0.098,0.004 -0.197,0.046 -0.294,0.046 -1.496,0 -2.826,-0.303 -3.83,-0.89 l 1.089,-2.128 0.454,-0.887 -0.891,-0.452 -2.136,-1.088 c 0.508,-1.151 1.515,-2.25 2.818,-3.143 -0.287,-0.219 -0.561,-0.441 -0.81,-0.669 -1.687,1.217 -2.846,2.755 -3.235,4.31 l 2.908,1.483 -1.482,2.843 c 1.221,1.023 3.049,1.522 5.114,1.522 z m 27.806,-5.846 c -0.39,-1.555 -1.548,-3.093 -3.234,-4.311 -0.25,0.228 -0.523,0.451 -0.81,0.669 1.304,0.893 2.31,1.992 2.817,3.145 l -2.136,1.088 -0.891,0.453 0.454,0.892 1.089,2.137 c -1.004,0.587 -2.332,0.904 -3.828,0.904 -0.099,0 -0.199,-0.01 -0.299,-0.013 0.103,0.344 0.192,0.683 0.26,1.011 l 0.039,0.002 c 2.066,0 3.892,-0.563 5.112,-1.587 l -1.482,-2.908 z m -12.653,9.182 c -0.447,1.5170001 -1.181,2.8120001 -2.119,3.6510001 l -1.695,-1.694 -0.707,-0.707 -0.707,0.707 -1.695,1.694 c -0.938,-0.839 -1.673,-2.136 -2.12,-3.6520001 -0.296,0.2060001 -0.593,0.3970001 -0.886,0.5630001 0.636,1.98 1.741,3.559 3.1,4.409 l 2.308,-2.307 2.308,2.308 c 1.358,-0.851 2.464,-2.428 3.101,-4.408 -0.295,-0.168 -0.591,-0.359 -0.888,-0.5640001 z"
-       fill="#ea596e"
-       id="path4-3" />
-    <path
-       fill="#ea596e"
-       d="m 56.41233,-31.002714 c 0.426,1.146 0.748,2.596 0.841,4.284 l 0.2,3.683 3.564,-0.946 c 1.32,-0.351 2.655,-0.536 3.86,-0.536 0.16,0 0.318,0.003 0.474,0.01 l -1.827,2.819 3.139,1.211 c -0.958,0.759 -2.237,1.514 -3.814,2.123 l -3.441,1.328 2.001,3.099 c 0.918,1.42 1.509,2.782 1.838,3.96 l -3.244,-0.865 -0.182,3.357 c -1.019,-0.677 -2.132,-1.66 -3.198,-2.973 l -2.329,-2.863 -2.328,2.862 c -1.066,1.312 -2.179,2.295 -3.198,2.972 l -0.18,-3.354 -3.248,0.864 c 0.329,-1.178 0.921,-2.54 1.839,-3.961 l 2.004,-3.099 -3.442,-1.328 c -1.577,-0.609 -2.856,-1.363 -3.814,-2.122 l 3.135,-1.208 -1.827,-2.823 c 0.155,-0.006 0.313,-0.01 0.473,-0.01 1.206,0 2.541,0.185 3.861,0.536 l 3.564,0.947 0.202,-3.683 c 0.092,-1.688 0.415,-3.138 0.84,-4.284 l 2.119,2.609 2.118,-2.609 m 0.19,-4.991 -2.308,2.841 -2.308,-2.841 c -1.989,1.532 -3.421,4.992 -3.646,9.112 -1.617,-0.43 -3.192,-0.637 -4.632,-0.637 -2.11,0 -3.929,0.445 -5.161,1.289 l 1.989,3.073 -3.415,1.316 c 0.842,2.366 3.69,4.797 7.54,6.283 -2.241,3.465 -3.116,7.106 -2.407,9.5160001 l 3.537,-0.9410001 0.196,3.6540001 c 2.512,-0.07 5.703,-2.027 8.307,-5.2280001 2.603,3.2010001 5.796,5.1580001 8.306,5.2280001 l 0.198,-3.6550001 3.535,0.9430001 c 0.71,-2.4110001 -0.165,-6.0500001 -2.404,-9.5170001 3.849,-1.485 6.696,-3.918 7.538,-6.283 l -3.415,-1.318 1.99,-3.07 c -1.233,-0.844 -3.053,-1.29 -5.164,-1.29 -1.438,0 -3.013,0.207 -4.63,0.636 -0.225,-4.119 -1.657,-7.579 -3.646,-9.111 z"
-       id="path6-6" />
-  </g>
-  <text
-     xml:space="preserve"
-     style="font-style:normal;font-weight:normal;font-size:42.6667px;line-height:1.25;font-family:sans-serif;fill:#ea596e;fill-opacity:1;stroke:none"
-     x="2.2188232"
-     y="31.430677"
-     id="text46212"><tspan
-       sodipodi:role="line"
-       id="tspan46210"
-       x="2.2188232"
-       y="31.430677"
-       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:42.6667px;font-family:'TeX Gyre Termes';-inkscape-font-specification:'TeX Gyre Termes'">D</tspan></text>
-  <text
-     xml:space="preserve"
-     style="font-style:normal;font-weight:normal;font-size:42.6667px;line-height:1.25;font-family:sans-serif;fill:#ea596e;fill-opacity:1;stroke:none"
-     x="41.347008"
-     y="67.114784"
-     id="text46212-1"><tspan
-       sodipodi:role="line"
-       id="tspan46210-5"
-       x="41.347008"
-       y="67.114784"
-       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:42.6667px;font-family:'TeX Gyre Termes';-inkscape-font-specification:'TeX Gyre Termes'">F</tspan></text>
-</svg>
@@ -1,537 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<svg
-   width="850"
-   height="480"
-   viewBox="0 0 224.89584 127"
-   version="1.1"
-   id="svg8"
-   inkscape:version="1.2 (dc2aedaf03, 2022-05-15)"
-   sodipodi:docname="garage_tables.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg"
-   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-   xmlns:cc="http://creativecommons.org/ns#"
-   xmlns:dc="http://purl.org/dc/elements/1.1/">
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="marker1262"
-       refX="0"
-       refY="0"
-       orient="auto"
-       inkscape:stockid="Arrow1Mend"
-       inkscape:isstock="true">
-      <path
-         transform="matrix(-0.4,0,0,-0.4,-4,0)"
-         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1"
-         d="M 0,0 5,-5 -12.5,0 5,5 Z"
-         id="path1260" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow1Mend"
-       refX="0"
-       refY="0"
-       orient="auto"
-       inkscape:stockid="Arrow1Mend"
-       inkscape:isstock="true"
-       inkscape:collect="always">
-      <path
-         transform="matrix(-0.4,0,0,-0.4,-4,0)"
-         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1"
-         d="M 0,0 5,-5 -12.5,0 5,5 Z"
-         id="path965" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow1Lend"
-       refX="0"
-       refY="0"
-       orient="auto"
-       inkscape:stockid="Arrow1Lend"
-       inkscape:isstock="true">
-      <path
-         transform="matrix(-0.8,0,0,-0.8,-10,0)"
-         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1"
-         d="M 0,0 5,-5 -12.5,0 5,5 Z"
-         id="path959" />
-    </marker>
-  </defs>
-  <sodipodi:namedview
-     id="base"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:pageopacity="0.0"
-     inkscape:pageshadow="2"
-     inkscape:zoom="0.98994949"
-     inkscape:cx="429.31483"
-     inkscape:cy="289.40871"
-     inkscape:document-units="mm"
-     inkscape:current-layer="layer1"
-     inkscape:document-rotation="0"
-     showgrid="false"
-     units="px"
-     inkscape:window-width="1678"
-     inkscape:window-height="993"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:showpageshadow="2"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1" />
-  <metadata
-     id="metadata5">
-    <rdf:RDF>
-      <cc:Work
-         rdf:about="">
-        <dc:format>image/svg+xml</dc:format>
-        <dc:type
-           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
-        <dc:title />
-      </cc:Work>
-    </rdf:RDF>
-  </metadata>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1">
-    <text
-       xml:space="preserve"
-       style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-       x="39.570904"
-       y="38.452755"
-       id="text2025"><tspan
-         sodipodi:role="line"
-         id="tspan2023"
-         x="39.570904"
-         y="38.452755"
-         style="font-size:5.64444px;stroke-width:0.264583" /></text>
-    <text
-       xml:space="preserve"
-       style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-       x="101.95796"
-       y="92.835831"
-       id="text2139"><tspan
-         sodipodi:role="line"
-         id="tspan2137"
-         x="101.95796"
-         y="92.835831"
-         style="stroke-width:0.264583"> </tspan></text>
-    <g
-       id="g2316"
-       transform="translate(-11.455511,1.5722486)">
-      <g
-         id="g2277">
-        <rect
-           style="fill:none;stroke:#000000;stroke-width:0.8;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-           id="rect833"
-           width="47.419891"
-           height="95.353409"
-           x="18.534418"
-           y="24.42766" />
-        <rect
-           style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-           id="rect833-3"
-           width="47.419891"
-           height="86.973076"
-           x="18.534418"
-           y="32.807987" />
-        <text
-           xml:space="preserve"
-           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-           x="32.250839"
-           y="29.894743"
-           id="text852"><tspan
-             sodipodi:role="line"
-             id="tspan850"
-             x="32.250839"
-             y="29.894743"
-             style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Object</tspan></text>
-      </g>
-      <g
-         id="g2066"
-         transform="translate(-2.1807817,-3.0621439)">
-        <g
-           id="g1969"
-           transform="matrix(0.12763631,0,0,0.12763631,0.7215051,24.717273)"
-           style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-opacity:1">
-          <path
-             style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-width:0.264583;stroke-opacity:1"
-             d="m 203.71837,154.80038 c -1.11451,3.75057 -2.45288,5.84095 -5.11132,7.98327 -2.2735,1.83211 -4.66721,2.65982 -8.09339,2.79857 -2.59227,0.10498 -2.92868,0.0577 -5.02863,-0.70611 -3.99215,-1.45212 -7.1627,-4.65496 -8.48408,-8.57046 -1.28374,-3.80398 -0.61478,-8.68216 1.64793,-12.01698 0.87317,-1.28689 3.15089,-3.48326 4.18771,-4.03815 l 0.53332,-28.51234 5.78454,-5.09197 6.95158,6.16704 -3.21112,3.49026 3.17616,3.45499 -3.17616,3.40822 2.98973,3.28645 -3.24843,3.3829 4.49203,4.58395 0.0516,5.69106 c 1.06874,0.64848 3.81974,3.24046 4.69548,4.56257 0.452,0.68241 1.06834,2.0197 1.36962,2.97176 0.62932,1.98864 0.88051,5.785 0.47342,7.15497 z m -10.0406,2.32604 c -0.88184,-3.17515 -4.92402,-3.78864 -6.75297,-1.02492 -0.58328,0.8814 -0.6898,1.28852 -0.58362,2.23056 0.26492,2.35041 2.45434,3.95262 4.60856,3.37255 1.19644,-0.32217 2.39435,-1.44872 2.72875,-2.56621 0.30682,-1.02529 0.30686,-0.9045 -7.9e-4,-2.01198 z"
-             id="path1971"
-             sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
-        </g>
-        <text
-           xml:space="preserve"
-           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-           x="28.809687"
-           y="44.070885"
-           id="text852-9"><tspan
-             sodipodi:role="line"
-             id="tspan850-4"
-             x="28.809687"
-             y="44.070885"
-             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">bucket </tspan></text>
-      </g>
-      <g
-         id="g2066-7"
-         transform="translate(-2.1807817,6.2627616)">
-        <g
-           id="g1969-8"
-           transform="matrix(0.12763631,0,0,0.12763631,0.7215051,24.717273)"
-           style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-opacity:1">
-          <path
-             style="fill:#4040ff;fill-opacity:1;stroke:none;stroke-width:0.264583;stroke-opacity:1"
-             d="m 203.71837,154.80038 c -1.11451,3.75057 -2.45288,5.84095 -5.11132,7.98327 -2.2735,1.83211 -4.66721,2.65982 -8.09339,2.79857 -2.59227,0.10498 -2.92868,0.0577 -5.02863,-0.70611 -3.99215,-1.45212 -7.1627,-4.65496 -8.48408,-8.57046 -1.28374,-3.80398 -0.61478,-8.68216 1.64793,-12.01698 0.87317,-1.28689 3.15089,-3.48326 4.18771,-4.03815 l 0.53332,-28.51234 5.78454,-5.09197 6.95158,6.16704 -3.21112,3.49026 3.17616,3.45499 -3.17616,3.40822 2.98973,3.28645 -3.24843,3.3829 4.49203,4.58395 0.0516,5.69106 c 1.06874,0.64848 3.81974,3.24046 4.69548,4.56257 0.452,0.68241 1.06834,2.0197 1.36962,2.97176 0.62932,1.98864 0.88051,5.785 0.47342,7.15497 z m -10.0406,2.32604 c -0.88184,-3.17515 -4.92402,-3.78864 -6.75297,-1.02492 -0.58328,0.8814 -0.6898,1.28852 -0.58362,2.23056 0.26492,2.35041 2.45434,3.95262 4.60856,3.37255 1.19644,-0.32217 2.39435,-1.44872 2.72875,-2.56621 0.30682,-1.02529 0.30686,-0.9045 -7.9e-4,-2.01198 z"
-             id="path1971-4"
-             sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
-        </g>
-        <text
-           xml:space="preserve"
-           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-           x="28.809687"
-           y="44.070885"
-           id="text852-9-5"><tspan
-             sodipodi:role="line"
-             id="tspan850-4-0"
-             x="28.809687"
-             y="44.070885"
-             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">file path </tspan></text>
-        <path
-           style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-width:0.0337704;stroke-opacity:1"
-           d="m 174.20027,104.45585 c -0.14225,0.47871 -0.31308,0.74552 -0.65239,1.01896 -0.29018,0.23384 -0.5957,0.33949 -1.03301,0.3572 -0.33087,0.0134 -0.37381,0.007 -0.64184,-0.0901 -0.50954,-0.18534 -0.91422,-0.59414 -1.08287,-1.0939 -0.16385,-0.48552 -0.0785,-1.10816 0.21033,-1.5338 0.11145,-0.16426 0.40217,-0.44459 0.53451,-0.51542 l 0.0681,-3.639207 0.73832,-0.64992 0.88727,0.787138 -0.40986,0.445484 0.4054,0.440982 -0.4054,0.435013 0.3816,0.41947 -0.41461,0.43178 0.57334,0.58508 0.007,0.72639 c 0.13641,0.0828 0.48753,0.4136 0.59931,0.58235 0.0577,0.0871 0.13636,0.25778 0.17481,0.3793 0.0803,0.25382 0.11239,0.73838 0.0604,0.91323 z m -1.28154,0.29689 c -0.11256,-0.40526 -0.62849,-0.48357 -0.86193,-0.13082 -0.0745,0.1125 -0.088,0.16447 -0.0745,0.2847 0.0338,0.3 0.31326,0.5045 0.58822,0.43046 0.15271,-0.0411 0.30561,-0.1849 0.34829,-0.32754 0.0392,-0.13086 0.0392,-0.11544 -1e-4,-0.2568 z"
-           id="path1971-3"
-           sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
-        <text
-           xml:space="preserve"
-           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-           x="177.8474"
-           y="104.05132"
-           id="text852-9-6"><tspan
-             sodipodi:role="line"
-             id="tspan850-4-7"
-             x="177.8474"
-             y="104.05132"
-             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">= partition key </tspan></text>
-        <path
-           style="fill:#4040ff;fill-opacity:1;stroke:none;stroke-width:0.0337704;stroke-opacity:1"
-           d="m 174.20027,113.78076 c -0.14225,0.47871 -0.31308,0.74552 -0.65239,1.01895 -0.29018,0.23385 -0.5957,0.33949 -1.03301,0.3572 -0.33087,0.0134 -0.37381,0.007 -0.64184,-0.0901 -0.50954,-0.18534 -0.91422,-0.59414 -1.08287,-1.0939 -0.16385,-0.48553 -0.0785,-1.10816 0.21033,-1.53381 0.11145,-0.16425 0.40217,-0.44459 0.53451,-0.51541 l 0.0681,-3.63921 0.73832,-0.64992 0.88727,0.78714 -0.40986,0.44548 0.4054,0.44098 -0.4054,0.43502 0.3816,0.41947 -0.41461,0.43178 0.57334,0.58508 0.007,0.72638 c 0.13641,0.0828 0.48753,0.4136 0.59931,0.58235 0.0577,0.0871 0.13636,0.25779 0.17481,0.37931 0.0803,0.25382 0.11239,0.73837 0.0604,0.91323 z m -1.28154,0.29689 c -0.11256,-0.40527 -0.62849,-0.48357 -0.86193,-0.13082 -0.0745,0.1125 -0.088,0.16446 -0.0745,0.2847 0.0338,0.3 0.31326,0.5045 0.58822,0.43046 0.15271,-0.0411 0.30561,-0.18491 0.34829,-0.32754 0.0392,-0.13087 0.0392,-0.11545 -1e-4,-0.2568 z"
-           id="path1971-4-5"
-           sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
-        <text
-           xml:space="preserve"
-           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-           x="177.8474"
-           y="113.37622"
-           id="text852-9-5-3"><tspan
-             sodipodi:role="line"
-             id="tspan850-4-0-5"
-             x="177.8474"
-             y="113.37622"
-             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">= sort key </tspan></text>
-      </g>
-      <g
-         id="g2161"
-         transform="translate(-62.264403,-59.333115)">
-        <g
-           id="g2271"
-           transform="translate(0,67.042823)">
-          <rect
-             style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-             id="rect833-6"
-             width="39.008453"
-             height="16.775949"
-             x="84.896881"
-             y="90.266838" />
-          <rect
-             style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-             id="rect833-3-1"
-             width="39.008453"
-             height="8.673645"
-             x="84.896881"
-             y="98.369141" />
-          <text
-             xml:space="preserve"
-             style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-             x="89.826942"
-             y="96.212921"
-             id="text852-0"><tspan
-               sodipodi:role="line"
-               id="tspan850-6"
-               x="89.826942"
-               y="96.212921"
-               style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Version 1</tspan></text>
-          <text
-             xml:space="preserve"
-             style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-             x="89.826942"
-             y="104.71013"
-             id="text852-0-3"><tspan
-               sodipodi:role="line"
-               id="tspan850-6-2"
-               x="89.826942"
-               y="104.71013"
-               style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#4d4d4d;stroke-width:0.264583">deleted</tspan></text>
-        </g>
-      </g>
-      <g
-         id="g2263"
-         transform="translate(0,-22.791204)">
-        <g
-           id="g2161-1"
-           transform="translate(-62.264403,-10.910843)">
-          <rect
-             style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-             id="rect833-6-5"
-             width="39.008453"
-             height="36.749603"
-             x="84.896881"
-             y="90.266838" />
-          <rect
-             style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-             id="rect833-3-1-5"
-             width="39.008453"
-             height="28.647301"
-             x="84.896881"
-             y="98.369141" />
-          <text
-             xml:space="preserve"
-             style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-             x="89.826942"
-             y="96.212921"
-             id="text852-0-4"><tspan
-               sodipodi:role="line"
-               id="tspan850-6-7"
-               x="89.826942"
-               y="96.212921"
-               style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Version 2</tspan></text>
-          <text
-             xml:space="preserve"
-             style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-             x="89.826942"
-             y="104.71013"
-             id="text852-0-3-6"><tspan
-               sodipodi:role="line"
-               id="tspan850-6-2-5"
-               x="89.826942"
-               y="104.71013"
-               style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#000000;stroke-width:0.264583">id</tspan></text>
-        </g>
-        <text
-           xml:space="preserve"
-           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-           x="27.56254"
-           y="100.34132"
-           id="text852-0-3-6-6"><tspan
-             sodipodi:role="line"
-             id="tspan850-6-2-5-9"
-             x="27.56254"
-             y="100.34132"
-             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#000000;stroke-width:0.264583">size</tspan></text>
-        <text
-           xml:space="preserve"
-           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-           x="27.56254"
-           y="106.90263"
-           id="text852-0-3-6-6-3"><tspan
-             sodipodi:role="line"
-             id="tspan850-6-2-5-9-7"
-             x="27.56254"
-             y="106.90263"
-             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#000000;stroke-width:0.264583">MIME type</tspan></text>
-        <text
-           xml:space="preserve"
-           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-           x="27.56254"
-           y="111.92816"
-           id="text852-0-3-6-6-3-4"><tspan
-             sodipodi:role="line"
-             id="tspan850-6-2-5-9-7-5"
-             x="27.56254"
-             y="111.92816"
-             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#000000;stroke-width:0.264583">...</tspan></text>
-      </g>
-    </g>
-    <g
-       id="g898"
-       transform="translate(-6.2484318,29.95006)">
-      <rect
-         style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-         id="rect833-7"
-         width="47.419891"
-         height="44.007515"
-         x="95.443573"
-         y="24.42766" />
-      <rect
-         style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-         id="rect833-3-4"
-         width="47.419891"
-         height="35.627186"
-         x="95.443573"
-         y="32.807987" />
-      <text
-         xml:space="preserve"
-         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-         x="107.46638"
-         y="29.894743"
-         id="text852-4"><tspan
-           sodipodi:role="line"
-           id="tspan850-3"
-           x="107.46638"
-           y="29.894743"
-           style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Version</tspan></text>
-      <path
-         style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-width:0.0337704;stroke-opacity:1"
-         d="m 102.90563,41.413279 c -0.14226,0.478709 -0.31308,0.745518 -0.65239,1.018956 -0.29019,0.233843 -0.59571,0.339489 -1.03301,0.357199 -0.33087,0.0134 -0.37381,0.0074 -0.64184,-0.09013 -0.50954,-0.185343 -0.914221,-0.594142 -1.082877,-1.093901 -0.163852,-0.485526 -0.07847,-1.108159 0.210335,-1.533803 0.111448,-0.164254 0.402172,-0.444591 0.534502,-0.515415 l 0.0681,-3.63921 0.73832,-0.64992 0.88727,0.787138 -0.40985,0.445484 0.40539,0.440982 -0.40539,0.435013 0.3816,0.41947 -0.41462,0.431781 0.57335,0.585078 0.007,0.726386 c 0.13641,0.08277 0.48753,0.413601 0.59931,0.58235 0.0577,0.0871 0.13636,0.257787 0.17481,0.379304 0.0803,0.253823 0.11239,0.738377 0.0604,0.913234 z m -1.28155,0.296888 c -0.11255,-0.405265 -0.62848,-0.483569 -0.86192,-0.130817 -0.0744,0.112498 -0.088,0.164461 -0.0745,0.2847 0.0338,0.299998 0.31326,0.504498 0.58822,0.43046 0.15271,-0.04112 0.3056,-0.184909 0.34828,-0.327542 0.0392,-0.130864 0.0392,-0.115447 -1e-4,-0.256801 z"
-         id="path1971-0"
-         sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
-      <text
-         xml:space="preserve"
-         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-         x="104.99195"
-         y="41.008743"
-         id="text852-9-7"><tspan
-           sodipodi:role="line"
-           id="tspan850-4-8"
-           x="104.99195"
-           y="41.008743"
-           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">id </tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-         x="104.99195"
-         y="49.168018"
-         id="text852-9-7-6"><tspan
-           sodipodi:role="line"
-           id="tspan850-4-8-8"
-           x="104.99195"
-           y="49.168018"
-           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">h(block 1)</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-         x="104.99195"
-         y="56.583336"
-         id="text852-9-7-6-8"><tspan
-           sodipodi:role="line"
-           id="tspan850-4-8-8-4"
-           x="104.99195"
-           y="56.583336"
-           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">h(block 2)</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-         x="104.99195"
-         y="64.265732"
-         id="text852-9-7-6-3"><tspan
-           sodipodi:role="line"
-           id="tspan850-4-8-8-1"
-           x="104.99195"
-           y="64.265732"
-           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">...</tspan></text>
-    </g>
-    <g
-       id="g898-3"
-       transform="translate(75.777779,38.888663)">
-      <rect
-         style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-         id="rect833-7-6"
-         width="47.419891"
-         height="29.989157"
-         x="95.443573"
-         y="24.42766" />
-      <rect
-         style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
-         id="rect833-3-4-7"
-         width="47.419891"
-         height="21.608831"
-         x="95.443573"
-         y="32.807987" />
-      <text
-         xml:space="preserve"
-         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-         x="102.11134"
-         y="29.894743"
-         id="text852-4-5"><tspan
-           sodipodi:role="line"
-           id="tspan850-3-3"
-           x="102.11134"
-           y="29.894743"
-           style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Data block</tspan></text>
-      <path
-         style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-width:0.0337704;stroke-opacity:1"
-         d="m 102.90563,41.413279 c -0.14226,0.478709 -0.31308,0.745518 -0.65239,1.018956 -0.29019,0.233843 -0.59571,0.339489 -1.03301,0.357199 -0.33087,0.0134 -0.37381,0.0074 -0.64184,-0.09013 -0.50954,-0.185343 -0.914221,-0.594142 -1.082877,-1.093901 -0.163852,-0.485526 -0.07847,-1.108159 0.210335,-1.533803 0.111448,-0.164254 0.402172,-0.444591 0.534502,-0.515415 l 0.0681,-3.63921 0.73832,-0.64992 0.88727,0.787138 -0.40985,0.445484 0.40539,0.440982 -0.40539,0.435013 0.3816,0.41947 -0.41462,0.431781 0.57335,0.585078 0.007,0.726386 c 0.13641,0.08277 0.48753,0.413601 0.59931,0.58235 0.0577,0.0871 0.13636,0.257787 0.17481,0.379304 0.0803,0.253823 0.11239,0.738377 0.0604,0.913234 z m -1.28155,0.296888 c -0.11255,-0.405265 -0.62848,-0.483569 -0.86192,-0.130817 -0.0744,0.112498 -0.088,0.164461 -0.0745,0.2847 0.0338,0.299998 0.31326,0.504498 0.58822,0.43046 0.15271,-0.04112 0.3056,-0.184909 0.34828,-0.327542 0.0392,-0.130864 0.0392,-0.115447 -1e-4,-0.256801 z"
-         id="path1971-0-5"
-         sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
-      <text
-         xml:space="preserve"
-         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-         x="104.99195"
-         y="41.008743"
-         id="text852-9-7-62"><tspan
-           sodipodi:role="line"
-           id="tspan850-4-8-9"
-           x="104.99195"
-           y="41.008743"
-           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">hash </tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-         x="104.99195"
-         y="49.168018"
-         id="text852-9-7-6-1"><tspan
-           sodipodi:role="line"
-           id="tspan850-4-8-8-2"
-           x="104.99195"
-           y="49.168018"
-           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">data</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow1Mend)"
-       d="M 42.105292,69.455903 89.563703,69.317144"
-       id="path954"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#marker1262)"
-       d="m 134.32612,77.363197 38.12618,0.260865"
-       id="path1258"
-       sodipodi:nodetypes="cc" />
-    <text
-       xml:space="preserve"
-       style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-       x="8.6727352"
-       y="16.687063"
-       id="text852-3"><tspan
-         sodipodi:role="line"
-         id="tspan850-67"
-         x="8.6727352"
-         y="16.687063"
-         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Objects table </tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-       x="89.190445"
-       y="16.687063"
-       id="text852-3-5"><tspan
-         sodipodi:role="line"
-         id="tspan850-67-3"
-         x="89.190445"
-         y="16.687063"
-         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Versions table </tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
-       x="174.55702"
-       y="16.687063"
-       id="text852-3-56"><tspan
-         sodipodi:role="line"
-         id="tspan850-67-2"
-         x="174.55702"
-         y="16.687063"
-         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Blocks table</tspan></text>
-  </g>
-</svg>
@@ -1,433 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="400"
-   viewBox="0 0 264.58333 105.83333"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="lattice1.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="445.81962"
-     inkscape:cy="222.66987"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
-       id="rect288"
-       width="209.84705"
-       height="104.42732"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-  </g>
-</svg>
@@ -1,514 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="400"
-   viewBox="0 0 264.58333 105.83333"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="lattice2.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="384.39345"
-     inkscape:cy="227.46879"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
-       id="rect288"
-       width="209.84705"
-       height="104.42732"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="139.48744"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="131.61919"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="stroke-width:0.264583;fill:#000000"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-  </g>
-</svg>
@@ -1,515 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="400"
-   viewBox="0 0 264.58333 105.83333"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="lattice3.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.4734708"
-     inkscape:cx="324.06479"
-     inkscape:cy="168.98876"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
-       id="rect288"
-       width="209.84705"
-       height="104.42732"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="139.48744"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="119.58919"
-       cy="67.645035"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="stroke-width:0.264583;fill:#000000"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-  </g>
-</svg>
@@ -1,525 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="400"
-   viewBox="0 0 264.58333 105.83333"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="lattice4.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="0.73673541"
-     inkscape:cx="287.07728"
-     inkscape:cy="294.54265"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
-       id="rect288"
-       width="209.84705"
-       height="104.42732"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="126.08154"
-       cy="67.968384"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="119.58919"
-       cy="67.645035"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="stroke-width:0.264583;fill:#000000"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="14.395845"
-       y="52.022549"
-       id="text4280"><tspan
-         sodipodi:role="line"
-         id="tspan4278"
-         style="fill:#000000;stroke-width:0.264583"
-         x="14.395845"
-         y="52.022549">return OK</tspan></text>
-  </g>
-</svg>
@@ -1,536 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="400"
-   viewBox="0 0 264.58333 105.83333"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="lattice5.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="276.89766"
-     inkscape:cy="254.34273"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
-       id="rect288"
-       width="209.84705"
-       height="104.42732"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="126.08154"
-       cy="67.968384"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="119.58919"
-       cy="67.645035"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="stroke-width:0.264583;fill:#000000"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.261436"
-       id="text3707-1"><tspan
-         sodipodi:role="line"
-         id="tspan3705-5"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.261436">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="14.395845"
-       y="52.022549"
-       id="text4280"><tspan
-         sodipodi:role="line"
-         id="tspan4278"
-         style="fill:#000000;stroke-width:0.264583"
-         x="14.395845"
-         y="52.022549">return OK</tspan></text>
-  </g>
-</svg>
@@ -1,553 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="400"
-   viewBox="0 0 264.58333 105.83333"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="lattice6.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="277.85744"
-     inkscape:cy="254.34273"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
-       id="rect288"
-       width="209.84705"
-       height="104.42732"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="126.08154"
-       cy="67.968384"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="119.58919"
-       cy="67.645035"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="stroke-width:0.264583;fill:#000000"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.261436"
-       id="text3707-1"><tspan
-         sodipodi:role="line"
-         id="tspan3705-5"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.261436">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-4"
-       cx="18.004833"
-       cy="70.942116"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="73.643356"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-65"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="73.643356">$\to \{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="14.395845"
-       y="52.022549"
-       id="text4280"><tspan
-         sodipodi:role="line"
-         id="tspan4278"
-         style="fill:#000000;stroke-width:0.264583"
-         x="14.395845"
-         y="52.022549">return OK</tspan></text>
-  </g>
-</svg>
@@ -1,581 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="400"
-   viewBox="0 0 264.58333 105.83333"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="lattice7.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="276.89766"
-     inkscape:cy="254.34273"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
-       id="rect288"
-       width="209.84705"
-       height="104.42732"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="126.08154"
-       cy="67.968384"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="119.58919"
-       cy="67.645035"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="stroke-width:0.264583;fill:#000000"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.261436"
-       id="text3707-1"><tspan
-         sodipodi:role="line"
-         id="tspan3705-5"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.261436">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-4"
-       cx="18.004833"
-       cy="70.942116"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="73.643356"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-65"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="73.643356">$\to \{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="14.395845"
-       y="52.022549"
-       id="text4280"><tspan
-         sodipodi:role="line"
-         id="tspan4278"
-         style="fill:#000000;stroke-width:0.264583"
-         x="14.395845"
-         y="52.022549">return OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="14.395845"
-       y="92.005798"
-       id="text4280-3"><tspan
-         sodipodi:role="line"
-         id="tspan4278-7"
-         style="fill:#000000;stroke-width:0.264583"
-         x="14.395845"
-         y="92.005798">return $\{\}\sqcup\{a\}=\{a\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-5"
-       cx="18.004833"
-       cy="81.007744"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="83.577797"
-       id="text3750-0-6"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-9"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="83.577797">$\to \{a\}$</tspan></text>
-  </g>
-</svg>
@@ -1,581 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="400"
-   viewBox="0 0 264.58333 105.83333"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="lattice8.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.4734708"
-     inkscape:cx="399.39712"
-     inkscape:cy="248.39311"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
-       id="rect288"
-       width="209.84705"
-       height="104.42732"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="stroke-width:0.264583;fill:#000000"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="stroke-width:0.264583;fill:#000000"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="stroke-width:0.264583;fill:#000000"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="stroke-width:0.264583;fill:#000000"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="132.33408"
-       cy="68.007973"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="126.08154"
-       cy="67.968384"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="119.58919"
-       cy="67.645035"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="stroke-width:0.264583;fill:#000000"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.261436"
-       id="text3707-1"><tspan
-         sodipodi:role="line"
-         id="tspan3705-5"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.261436">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-4"
-       cx="18.004833"
-       cy="70.942116"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="73.643356"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-65"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="73.643356">$\to \{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="14.395845"
-       y="52.022549"
-       id="text4280"><tspan
-         sodipodi:role="line"
-         id="tspan4278"
-         style="fill:#000000;stroke-width:0.264583"
-         x="14.395845"
-         y="52.022549">return OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="14.395845"
-       y="92.005798"
-       id="text4280-3"><tspan
-         sodipodi:role="line"
-         id="tspan4278-7"
-         style="fill:#000000;stroke-width:0.264583"
-         x="14.395845"
-         y="92.005798">return $\{\}\sqcup\{a\}=\{a\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-5"
-       cx="18.004833"
-       cy="81.007744"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="83.577797"
-       id="text3750-0-6"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-9"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="83.577797">$\to \{a\}$</tspan></text>
-  </g>
-</svg>
@@ -1,576 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_1.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="469.81422"
-     inkscape:cy="257.22209"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="141.05479"
-       cy="95.316383"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="134.56244"
-       cy="94.993034"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-  </g>
-</svg>
@@ -1,715 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_10.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="664.65036"
-     inkscape:cy="366.63745"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="176.97627"
-       cy="68.155472"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="59.340172"
-       y="118.94403"
-       id="text3707-5-3"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6"
-         style="fill:#000000;stroke-width:0.264583"
-         x="59.340172"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0"
-       cx="67.201363"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="127.6125"
-       id="text3750-9"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="127.6125">$\to \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="62.764446"
-       y="146.3129"
-       id="text4280-6"><tspan
-         sodipodi:role="line"
-         style="fill:#000000;stroke-width:0.264583"
-         x="62.764446"
-         y="146.3129"
-         id="tspan2630">return $\{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-7"
-       cx="67.201363"
-       cy="133.94179"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="136.59073"
-       id="text3750-3-6"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-0"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="136.59073">$\to \{\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0-6"
-       cx="174.36296"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="179.81555"
-       y="127.6125"
-       id="text3750-9-1"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3-8"
-         style="fill:#000000;stroke-width:0.264583"
-         x="179.81555"
-         y="127.6125">$\to \{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="162.7999"
-       y="118.94403"
-       id="text3707-5-3-7"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6-5"
-         style="fill:#000000;stroke-width:0.264583"
-         x="162.7999"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
-       x="134.97845"
-       y="132.58472"
-       id="text3899"><tspan
-         sodipodi:role="line"
-         id="tspan3897"
-         style="stroke-width:0.264583"
-         x="134.97845"
-         y="132.58472">;</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="169.92604"
-       y="146.3129"
-       id="text4280-6-7"><tspan
-         sodipodi:role="line"
-         style="fill:#000000;stroke-width:0.264583"
-         x="169.92604"
-         y="146.3129"
-         id="tspan2630-9">return $\{b\}$</tspan></text>
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-7-2"
-       cx="174.36296"
-       cy="133.94179"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="179.81555"
-       y="136.59073"
-       id="text3750-3-6-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-0-2"
-         style="fill:#000000;stroke-width:0.264583"
-         x="179.81555"
-         y="136.59073">$\to \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:end;text-anchor:end;fill:#ff0000;stroke-width:0.264583"
-       x="259.75"
-       y="135.53111"
-       id="text9043"><tspan
-         sodipodi:role="line"
-         id="tspan9041"
-         style="fill:#ff0000;stroke-width:0.264583"
-         x="259.75"
-         y="135.53111">${\Large\textbf{??!}}$~~~~~</tspan><tspan
-         sodipodi:role="line"
-         style="fill:#ff0000;stroke-width:0.264583"
-         x="259.75"
-         y="146.11446"
-         id="tspan9372">$\{a\} \not\sqsubseteq \{b\}$</tspan></text>
-  </g>
-</svg>
@@ -1,576 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_2.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.4734708"
-     inkscape:cx="586.70996"
-     inkscape:cy="321.01077"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="141.05479"
-       cy="95.316383"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-  </g>
-</svg>
@@ -1,576 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_3.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="2.0838024"
-     inkscape:cx="465.25525"
-     inkscape:cy="269.21938"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="176.97627"
-       cy="68.155472"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-  </g>
-</svg>
@@ -1,587 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_4.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="505.32622"
-     inkscape:cy="316.72869"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="176.97627"
-       cy="68.155472"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="59.340172"
-       y="118.94403"
-       id="text3707-5-3"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6"
-         style="fill:#000000;stroke-width:0.264583"
-         x="59.340172"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-  </g>
-</svg>
@@ -1,604 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_5.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.4734708"
-     inkscape:cx="408.21983"
-     inkscape:cy="319.65343"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="176.97627"
-       cy="68.155472"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="59.340172"
-       y="118.94403"
-       id="text3707-5-3"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6"
-         style="fill:#000000;stroke-width:0.264583"
-         x="59.340172"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0"
-       cx="67.201363"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="127.6125"
-       id="text3750-9"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="127.6125">$\to \{a\}$</tspan></text>
-  </g>
-</svg>
@@ -1,632 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_6.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.4734708"
-     inkscape:cx="408.21983"
-     inkscape:cy="319.65343"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="176.97627"
-       cy="68.155472"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="59.340172"
-       y="118.94403"
-       id="text3707-5-3"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6"
-         style="fill:#000000;stroke-width:0.264583"
-         x="59.340172"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0"
-       cx="67.201363"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="127.6125"
-       id="text3750-9"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="127.6125">$\to \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="62.764446"
-       y="146.3129"
-       id="text4280-6"><tspan
-         sodipodi:role="line"
-         style="fill:#000000;stroke-width:0.264583"
-         x="62.764446"
-         y="146.3129"
-         id="tspan2630">return $\{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-7"
-       cx="67.201363"
-       cy="133.94179"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="136.59073"
-       id="text3750-3-6"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-0"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="136.59073">$\to \{\}$</tspan></text>
-  </g>
-</svg>
@@ -1,654 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_7.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.4734708"
-     inkscape:cx="553.45515"
-     inkscape:cy="346.80022"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="176.97627"
-       cy="68.155472"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="59.340172"
-       y="118.94403"
-       id="text3707-5-3"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6"
-         style="fill:#000000;stroke-width:0.264583"
-         x="59.340172"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0"
-       cx="67.201363"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="127.6125"
-       id="text3750-9"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="127.6125">$\to \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="62.764446"
-       y="146.3129"
-       id="text4280-6"><tspan
-         sodipodi:role="line"
-         style="fill:#000000;stroke-width:0.264583"
-         x="62.764446"
-         y="146.3129"
-         id="tspan2630">return $\{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-7"
-       cx="67.201363"
-       cy="133.94179"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="136.59073"
-       id="text3750-3-6"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-0"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="136.59073">$\to \{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="162.7999"
-       y="118.94403"
-       id="text3707-5-3-7"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6-5"
-         style="fill:#000000;stroke-width:0.264583"
-         x="162.7999"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
-       x="134.97845"
-       y="132.58472"
-       id="text3899"><tspan
-         sodipodi:role="line"
-         id="tspan3897"
-         style="stroke-width:0.264583"
-         x="134.97845"
-         y="132.58472">;</tspan></text>
-  </g>
-</svg>
@@ -1,671 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_8.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.4734708"
-     inkscape:cx="448.94001"
-     inkscape:cy="322.36811"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="176.97627"
-       cy="68.155472"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="59.340172"
-       y="118.94403"
-       id="text3707-5-3"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6"
-         style="fill:#000000;stroke-width:0.264583"
-         x="59.340172"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0"
-       cx="67.201363"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="127.6125"
-       id="text3750-9"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="127.6125">$\to \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="62.764446"
-       y="146.3129"
-       id="text4280-6"><tspan
-         sodipodi:role="line"
-         style="fill:#000000;stroke-width:0.264583"
-         x="62.764446"
-         y="146.3129"
-         id="tspan2630">return $\{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-7"
-       cx="67.201363"
-       cy="133.94179"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="136.59073"
-       id="text3750-3-6"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-0"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="136.59073">$\to \{\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0-6"
-       cx="174.36296"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="179.81555"
-       y="127.6125"
-       id="text3750-9-1"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3-8"
-         style="fill:#000000;stroke-width:0.264583"
-         x="179.81555"
-         y="127.6125">$\to \{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="162.7999"
-       y="118.94403"
-       id="text3707-5-3-7"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6-5"
-         style="fill:#000000;stroke-width:0.264583"
-         x="162.7999"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
-       x="134.97845"
-       y="132.58472"
-       id="text3899"><tspan
-         sodipodi:role="line"
-         id="tspan3897"
-         style="stroke-width:0.264583"
-         x="134.97845"
-         y="132.58472">;</tspan></text>
-  </g>
-</svg>
@@ -1,699 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
-
-<svg
-   width="1000"
-   height="600"
-   viewBox="0 0 264.58333 158.75"
-   version="1.1"
-   id="svg5"
-   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
-   sodipodi:docname="latticeB_9.svg"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:svg="http://www.w3.org/2000/svg">
-  <sodipodi:namedview
-     id="namedview7"
-     pagecolor="#ffffff"
-     bordercolor="#666666"
-     borderopacity="1.0"
-     inkscape:showpageshadow="2"
-     inkscape:pageopacity="0.0"
-     inkscape:pagecheckerboard="0"
-     inkscape:deskcolor="#d1d1d1"
-     inkscape:document-units="mm"
-     showgrid="false"
-     inkscape:zoom="1.0419012"
-     inkscape:cx="664.65036"
-     inkscape:cy="366.63745"
-     inkscape:window-width="1920"
-     inkscape:window-height="999"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
-     inkscape:current-layer="layer2" />
-  <defs
-     id="defs2">
-    <marker
-       style="overflow:visible"
-       id="Arrow2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-2"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-8" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-75-7-1"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-9-3-2" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-93-1-4"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-6-8-7" />
-    </marker>
-    <marker
-       style="overflow:visible"
-       id="Arrow2-9-7-2-8"
-       refX="0"
-       refY="0"
-       orient="auto-start-reverse"
-       inkscape:stockid="Arrow2"
-       markerWidth="7.6999998"
-       markerHeight="5.5999999"
-       viewBox="0 0 7.7 5.6"
-       inkscape:isstock="true"
-       inkscape:collect="always"
-       preserveAspectRatio="xMidYMid">
-      <path
-         transform="scale(0.7)"
-         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
-         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
-         id="arrow2L-1-0-6-4" />
-    </marker>
-  </defs>
-  <g
-     inkscape:label="Layer 1"
-     inkscape:groupmode="layer"
-     id="layer1"
-     sodipodi:insensitive="true">
-    <rect
-       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
-       id="rect288"
-       width="262.58151"
-       height="156.82782"
-       x="0.77790999"
-       y="0.93738818" />
-  </g>
-  <g
-     inkscape:groupmode="layer"
-     id="layer2"
-     inkscape:label="Layer 2">
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="99.307442"
-       id="text951"><tspan
-         sodipodi:role="line"
-         id="tspan949"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="99.307442">$\{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-       x="164.56372"
-       y="13.151893"
-       id="text1005"><tspan
-         sodipodi:role="line"
-         id="tspan1003"
-         style="fill:#000000;stroke-width:0.264583"
-         x="164.56372"
-         y="13.151893">$\{a,b,c\}$</tspan></text>
-    <g
-       id="g1175"
-       transform="translate(51.996784,3.5774043)">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="67.008698"
-         id="text1009"><tspan
-           sodipodi:role="line"
-           id="tspan1007"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="67.008698">$\{a\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="67.017166"
-         id="text1009-3"><tspan
-           sodipodi:role="line"
-           id="tspan1007-6"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="67.017166">$\{b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="67.008698"
-         id="text1009-7"><tspan
-           sodipodi:role="line"
-           id="tspan1007-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="67.008698">$\{c\}$</tspan></text>
-    </g>
-    <g
-       id="g1183"
-       transform="translate(51.996784,1.0317046)"
-       style="fill:#000000">
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="112.90984"
-         y="40.841526"
-         id="text1117"><tspan
-           sodipodi:role="line"
-           id="tspan1115"
-           style="fill:#000000;stroke-width:0.264583"
-           x="112.90984"
-           y="40.841526">$\{a,c\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="49.27084"
-         y="40.841526"
-         id="text1117-3"><tspan
-           sodipodi:role="line"
-           id="tspan1115-5"
-           style="fill:#000000;stroke-width:0.264583"
-           x="49.27084"
-           y="40.841526">$\{a,b\}$</tspan></text>
-      <text
-         xml:space="preserve"
-         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
-         x="176.20593"
-         y="40.841526"
-         id="text1117-6"><tspan
-           sodipodi:role="line"
-           id="tspan1115-2"
-           style="fill:#000000;stroke-width:0.264583"
-           x="176.20593"
-           y="40.841526">$\{b,c\}$</tspan></text>
-    </g>
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
-       d="M 153.33622,90.367682 118.34198,73.428915"
-       id="path1300" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
-       d="M 177.46016,90.367682 212.4544,73.428915"
-       id="path1300-2" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
-       d="M 153.33622,61.655656 118.34198,44.716889"
-       id="path1300-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
-       d="M 177.46016,61.655656 212.4544,44.716889"
-       id="path1300-2-6" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
-       d="M 118.34198,61.655656 153.33622,44.716889"
-       id="path1300-0-7" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
-       d="M 212.4544,61.655656 177.46016,44.716889"
-       id="path1300-2-6-9" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
-       d="M 118.34198,34.227412 153.33622,17.288645"
-       id="path1300-0-7-5" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
-       d="M 212.4544,34.227412 177.46016,17.288645"
-       id="path1300-2-6-9-0" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
-       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
-       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-9"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
-       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6"
-       sodipodi:nodetypes="cc" />
-    <path
-       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
-       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
-       id="path1300-2-2-6-9"
-       sodipodi:nodetypes="cc" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663"
-       cx="147.35568"
-       cy="95.24971"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3"
-       cx="176.97627"
-       cy="68.155472"
-       r="2.7302806" />
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1"
-       cx="18.004833"
-       cy="39.402473"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0"
-       cx="18.004833"
-       cy="30.371933"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6"
-       cx="18.004833"
-       cy="21.341394"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="13.702217"
-       id="text3707"><tspan
-         sodipodi:role="line"
-         id="tspan3705"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="13.702217">$write(\{a\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="24.042637"
-       id="text3750"><tspan
-         sodipodi:role="line"
-         id="tspan3748"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="33.02087"
-       id="text3750-3"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="41.972523"
-       id="text3750-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-1-4"
-       cx="18.004833"
-       cy="90.979645"
-       r="2.7302806" />
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-5"
-       cx="18.004833"
-       cy="81.949104"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-2"
-       cx="18.004833"
-       cy="72.918564"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="6.9525447"
-       y="65.279381"
-       id="text3707-5"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4"
-         style="fill:#000000;stroke-width:0.264583"
-         x="6.9525447"
-         y="65.279381">$write(\{b\})$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="59.340172"
-       y="118.94403"
-       id="text3707-5-3"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6"
-         style="fill:#000000;stroke-width:0.264583"
-         x="59.340172"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="75.619804"
-       id="text3750-7"><tspan
-         sodipodi:role="line"
-         id="tspan3748-4"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="23.457415"
-       y="84.598038"
-       id="text3750-3-4"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="23.457415"
-         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
-       x="23.457415"
-       y="93.54969"
-       id="text3750-0-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-6-7"
-         style="fill:#999999;stroke-width:0.264583"
-         x="23.457415"
-         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6"
-       cx="118.63729"
-       cy="67.630196"
-       r="2.7302806" />
-    <circle
-       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0"
-       cx="67.201363"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="127.6125"
-       id="text3750-9"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="127.6125">$\to \{a\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="62.764446"
-       y="146.3129"
-       id="text4280-6"><tspan
-         sodipodi:role="line"
-         style="fill:#000000;stroke-width:0.264583"
-         x="62.764446"
-         y="146.3129"
-         id="tspan2630">return $\{a\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-7"
-       cx="67.201363"
-       cy="133.94179"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="72.653946"
-       y="136.59073"
-       id="text3750-3-6"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-0"
-         style="fill:#000000;stroke-width:0.264583"
-         x="72.653946"
-         y="136.59073">$\to \{\}$</tspan></text>
-    <circle
-       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-6-6-0-6"
-       cx="174.36296"
-       cy="124.91125"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="179.81555"
-       y="127.6125"
-       id="text3750-9-1"><tspan
-         sodipodi:role="line"
-         id="tspan3748-3-8"
-         style="fill:#000000;stroke-width:0.264583"
-         x="179.81555"
-         y="127.6125">$\to \{\}$</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="162.7999"
-       y="118.94403"
-       id="text3707-5-3-7"><tspan
-         sodipodi:role="line"
-         id="tspan3705-4-6-5"
-         style="fill:#000000;stroke-width:0.264583"
-         x="162.7999"
-         y="118.94403">$read()$:</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
-       x="134.97845"
-       y="132.58472"
-       id="text3899"><tspan
-         sodipodi:role="line"
-         id="tspan3897"
-         style="stroke-width:0.264583"
-         x="134.97845"
-         y="132.58472">;</tspan></text>
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="169.92604"
-       y="146.3129"
-       id="text4280-6-7"><tspan
-         sodipodi:role="line"
-         style="fill:#000000;stroke-width:0.264583"
-         x="169.92604"
-         y="146.3129"
-         id="tspan2630-9">return $\{b\}$</tspan></text>
-    <circle
-       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
-       id="path3663-3-0-7-2"
-       cx="174.36296"
-       cy="133.94179"
-       r="2.7302806" />
-    <text
-       xml:space="preserve"
-       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
-       x="179.81555"
-       y="136.59073"
-       id="text3750-3-6-0"><tspan
-         sodipodi:role="line"
-         id="tspan3748-2-0-2"
-         style="fill:#000000;stroke-width:0.264583"
-         x="179.81555"
-         y="136.59073">$\to \{b\}$</tspan></text>
-  </g>
-</svg>
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Alex Auvolat	fd7d8fec59	Merge branch 'main' into next	2023-09-11 23:09:20 +02:00
Alex Auvolat	51abbb02d8	Merge branch 'main' into next	2023-09-11 20:00:02 +02:00
Alex Auvolat	ad6b1cc0be	Merge branch 'main' into next	2023-09-11 13:14:18 +02:00
Alex	7228fbfd4f	Merge pull request 'multi-hdd support (fix #218 )' (#625 ) from multihdd into next Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/625	2023-09-11 10:52:01 +00:00
Alex Auvolat	ba7ac52c19	block repair: simpler/more robust iterator progress calculation	2023-09-11 12:31:34 +02:00
Alex Auvolat	9526328d38	scrub: clear saved checkpoint when canceling scrub	2023-09-11 12:10:48 +02:00
Alex Auvolat	7f9ba49c71	block manager: remove data_dir field	2023-09-11 11:57:36 +02:00
Alex Auvolat	de5d792181	block manager: fix indentation (why not detected by cargo fmt?)	2023-09-11 11:52:57 +02:00
Alex Auvolat	be91ef6294	block manager: fix bug where rebalance didn't delete old copies	2023-09-07 16:04:03 +02:00
Alex Auvolat	2657b5c1b9	block manager: fix bugs	2023-09-07 15:30:56 +02:00
Alex Auvolat	eb972a8422	doc: update multi-hdd section	2023-09-07 14:48:36 +02:00
Alex Auvolat	2f112ac682	correct free data space accounting for multiple data dirs on same fs	2023-09-07 14:42:20 +02:00
Alex Auvolat	6a067e30ee	doc: documentation of rebalance repair	2023-09-07 13:49:12 +02:00
Alex Auvolat	6b008b5bd3	block manager: add rebalance operation to rebalance multi-hdd setups	2023-09-07 13:44:11 +02:00
Alex Auvolat	6595efd82f	Document multi-hdd support	2023-09-07 13:23:02 +02:00
Alex Auvolat	bca347a1e8	doc: update page on upgradin clusters	2023-09-07 12:52:44 +02:00
Alex Auvolat	99ed18350f	block manager: refactor and fix monitoring/statistics	2023-09-07 12:41:36 +02:00
Alex Auvolat	f38a31b330	block manager: avoid incorrect data_dir configs and avoid losing files	2023-09-06 17:49:30 +02:00
Alex Auvolat	e30865984a	block manager: scrub checkpointing	2023-09-06 16:35:28 +02:00
Alex Auvolat	55c514999e	block manager: fixes in layout	2023-09-06 16:35:28 +02:00
Alex Auvolat	a44f486931	block manager: refactoring & increase max worker count to 8	2023-09-06 16:35:28 +02:00
Alex Auvolat	3a74844df0	block manager: fix dir_not_empty	2023-09-06 16:35:28 +02:00
Alex Auvolat	93114a9747	block manager: refactoring	2023-09-06 16:35:28 +02:00
Alex Auvolat	fd00a47ddc	table queue: increase batch size	2023-09-06 16:35:28 +02:00
Alex Auvolat	1b8c265c14	block manager: get rid of check_block_status	2023-09-06 16:35:28 +02:00
Alex Auvolat	3199cab4c8	update cargo.nix	2023-09-06 16:35:28 +02:00
Alex Auvolat	a09f86729c	block manager: move blocks in write_block if necessary	2023-09-06 16:35:28 +02:00
Alex Auvolat	887b3233f4	block manager: use data paths from layout	2023-09-06 16:35:28 +02:00
Alex Auvolat	6c420c0880	block manager: multi-directory layout computation	2023-09-06 16:35:28 +02:00
Alex Auvolat	71c0188055	block manager: skeleton for multi-hdd support	2023-09-06 16:35:28 +02:00
Alex Auvolat	4b4f2000f4	lifecycle: fix SkipBucket bug	2023-09-06 16:34:07 +02:00
Alex	3f461d8891	Merge pull request 'object lifecycles (fix #309 )' (#620 ) from bucket-lifecycle into next Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/620	2023-09-04 09:45:10 +00:00
Alex Auvolat	8e0c020bb9	lifecycle worker: correct small clippy lints	2023-09-04 11:33:44 +02:00
Alex Auvolat	1cdc321e28	lifecycle worker: don't get stuck on non-existent bucket	2023-08-31 11:36:30 +02:00
Alex Auvolat	f579d6d9b4	lifecycle worker: fix potential inifinite loop	2023-08-31 11:29:54 +02:00
Alex Auvolat	a00a52633f	lifecycle worker: add log message when starting	2023-08-31 11:25:14 +02:00
Alex Auvolat	adbf5925de	lifecycle worker: use queue_insert and process objects in batches	2023-08-31 11:19:26 +02:00
Alex Auvolat	1cfcc61de8	lifecycle worker: mitigate potential bugs + refactoring	2023-08-31 00:28:37 +02:00
Alex Auvolat	be03a4610f	s3api: remove redundant serde rename attribute	2023-08-31 00:00:26 +02:00
Alex Auvolat	b2f679675e	lifecycle worker: take into account disabled rules	2023-08-30 23:52:09 +02:00
Alex Auvolat	5fad4c4658	update cargo.nix	2023-08-30 23:47:42 +02:00
Alex Auvolat	01c327a07a	lifecycle worker: avoid building chrono's serde feature	2023-08-30 23:46:15 +02:00
Alex Auvolat	f0a395e2e5	s3 bucket apis: remove redundant call	2023-08-30 23:39:28 +02:00
Alex Auvolat	d94f1c9178	reference manual: remove obsolete caveat about multipart uploads	2023-08-30 23:27:02 +02:00
Alex Auvolat	5c923d48d7	reference manual: document support for lifecycle configuration	2023-08-30 23:24:28 +02:00
Alex Auvolat	a1d57283c0	bucket_table: bucketparams::new doesn't need to be pub	2023-08-30 20:07:14 +02:00
Alex Auvolat	d2e94e36d6	lifecycle config: add missing line in merge() and remove tracing	2023-08-30 20:05:53 +02:00
Alex Auvolat	75ccc5a95c	lifecycle config: store date as given, try to debug	2023-08-30 20:02:07 +02:00
Alex Auvolat	7200954318	lifecycle worker: add logging	2023-08-30 14:54:52 +02:00
Alex Auvolat	0f1849e1ac	lifecycle worker: launch with the rest of Garage	2023-08-30 14:51:08 +02:00
Alex Auvolat	da8b224e24	lifecycle worker: skip entire bucket when no lifecycle config is set	2023-08-30 14:38:19 +02:00
Alex Auvolat	2996dc875f	lifecycle worker: implement main functionality	2023-08-30 14:29:03 +02:00
Alex Auvolat	a2e0e34db5	lifecycle: skeleton for lifecycle worker	2023-08-30 12:41:11 +02:00
Alex Auvolat	f7b409f114	use a NaiveDate in data model, it serializes to string (iso 8601 format)	2023-08-30 11:24:01 +02:00
Alex Auvolat	abf011c290	lifecycle: implement validation into garage's internal data structure	2023-08-29 18:22:03 +02:00
Alex Auvolat	8041d9a827	s3: add xml structures to serialize/deserialize lifecycle configs	2023-08-29 17:44:17 +02:00
Alex Auvolat	0b83e0558e	bucket_table: data model for lifecycle configuration	2023-08-29 17:00:41 +02:00
Alex Auvolat	2e90e1c124	Merge branch 'main' into next	2023-08-29 11:32:42 +02:00
Alex Auvolat	8ef42c9609	admin docs: reformatting, key admin: add check	2023-06-14 17:19:25 +02:00
Alex Auvolat	a83a092c03	admin: uniformize layout api and improve code	2023-06-14 17:12:37 +02:00
Alex Auvolat	7895f99d3a	admin and cli: hide secret keys unless asked	2023-06-14 16:56:15 +02:00
Alex Auvolat	4a82f6380e	admin api: move all endpoints to v1/ by default (v0/ still supported)	2023-06-14 14:15:51 +02:00
Alex Auvolat	28cc9f178a	admin api: make name optionnal for CreateKey	2023-06-14 13:56:37 +02:00
Alex Auvolat	2c83006608	admin api: fix doc in drafts	2023-06-14 13:54:34 +02:00
Alex Auvolat	35c108b85d	admin api: switch GetClusterHealth to camelcase (fix #381 again)	2023-06-14 13:53:19 +02:00
Alex Auvolat	52376d47ca	admin api: change cluster status/layout to use lists and not maps (fix #377 )	2023-06-14 13:45:27 +02:00
Alex Auvolat	187240e539	Merge branch 'main' into next	2023-06-14 13:02:46 +02:00
Alex Auvolat	5670367126	multipartupload in test: add forgotten timestamp	2023-06-13 23:10:46 +02:00
Alex Auvolat	cda957b4b1	update netapp's rmp-serde dependency to v1.1	2023-06-13 17:34:49 +02:00
Alex Auvolat	90b2d43eb4	Merge branch 'main' into next	2023-06-13 17:14:11 +02:00
Alex Auvolat	bf19a44fd9	admin API: add missing camelCase conversions (fix #381 )	2023-06-13 16:15:50 +02:00
Alex Auvolat	7126f3e1d1	garage key import: add checks and `--yes` CLI flag (fix #278 )	2023-06-13 15:56:48 +02:00
Alex Auvolat	942c1f1bfe	multipart uploads: save timestamp	2023-06-13 10:48:22 +02:00
Alex	0a06fda0da	Merge pull request 'Fix #204 (full Multipart Uploads semantics)' (#553 ) from nlnet-task1 into next Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/553	2023-06-09 15:34:09 +00:00
Alex Auvolat	3d477906d4	properly delete multipart uploads after completion	2023-06-09 17:13:27 +02:00
Alex Auvolat	e645bbd3ce	smoke test: add multipart upload test with part re-upload	2023-06-09 16:23:37 +02:00
Alex Auvolat	58563ed700	Add multipart upload using aws s3api	2023-06-09 16:23:37 +02:00
Alex Auvolat	a6cc563bdd	UploadPart: automatic cleanup of version (and reference blocked) when interrupted	2023-06-09 16:23:37 +02:00
Alex Auvolat	c14d3735e5	Add test for multipart uploads and fix part renumbering	2023-06-09 16:23:37 +02:00
Alex Auvolat	53bf2f070c	undo sort_key() returning Cow	2023-06-09 16:23:37 +02:00
Alex Auvolat	412ab77b08	comments and clippy lint fixes	2023-06-09 16:23:37 +02:00
Alex Auvolat	511e07ecd4	fix mpu counter (add missing workers) and report info at appropriate places	2023-06-09 16:23:37 +02:00
Alex Auvolat	4ea53dc759	Add multipart upload repair	2023-06-09 16:23:37 +02:00
Alex Auvolat	058518c22b	refactor repair workers with a trait	2023-06-09 16:23:37 +02:00
Alex Auvolat	8644376ac2	fix test; simplify code	2023-06-09 16:23:37 +02:00
Alex Auvolat	7ad7dae5d4	fix s3 list test	2023-06-09 16:23:37 +02:00
Alex Auvolat	75a0e01372	fix online repair	2023-06-09 16:23:37 +02:00
Alex Auvolat	bb176ebcb8	cargo fmt	2023-06-09 16:23:37 +02:00
Alex Auvolat	c1e1764f17	move git-version dependency to main crate to reduce rebuilds	2023-06-09 16:23:37 +02:00
Alex Auvolat	87be8eeb93	updaet block admin for new multipartupload models	2023-06-09 16:23:37 +02:00
Alex Auvolat	82e75c0e29	Adapt S3 API code to use new multipart upload models - Create and PutPart - completemultipartupload - upload part copy - list_parts	2023-06-09 16:23:37 +02:00
Alex Auvolat	38d6ac4295	New multipart upload table layout	2023-06-09 16:23:37 +02:00
Alex Auvolat	6005491cd8	Use Cow<[u8]> for sort keys	2023-06-09 16:23:37 +02:00
Alex Auvolat	ea3bfd2ab1	Minio tests for multipart upload behaviour: - upload part renumbering test - part skipping test	2023-06-09 16:23:37 +02:00
Alex Auvolat	e7e164a280	Make fsync an option for meta and data	2023-06-09 16:23:21 +02:00
Alex Auvolat	1e466b11eb	Revert integration tests to using Sled as LMDB causes failures	2023-06-09 13:23:08 +02:00
Alex Auvolat	865f0c7d0c	Add LMDB to debug builds	2023-06-09 12:04:28 +02:00
Alex Auvolat	906fe78b24	Integration tests: print logs when fails	2023-06-09 12:03:44 +02:00
Alex Auvolat	8a74e1c2bd	Split garage/admin.rs into smaller files	2023-06-06 15:39:15 +02:00
Alex Auvolat	19639705e6	Mark sled as deprecated, make lmdb default, and improve sqlite and lmdb defaults	2023-05-17 14:30:53 +02:00
Alex Auvolat	351d734e6c	Merge branch 'main' into next	2023-05-09 12:40:08 +02:00
Alex Auvolat	a1fcf1b175	Merge branch 'main' into next	2023-04-25 16:58:57 +02:00
Alex Auvolat	fa78d806e3	Merge branch 'main' into next	2023-04-25 12:34:26 +02:00
Alex Auvolat	654999e254	Update Cargo.nix	2023-01-26 15:50:54 +01:00
Jonathan Davies	db56d4658f	util/Cargo.toml: Updated rmp-serde from 0.15 to 1.1.	2023-01-26 11:03:43 +00:00
Alex Auvolat	12a4e1f303	Merge branch 'optimal-layout' into next	2023-01-11 17:50:42 +01:00
Alex Auvolat	84b4a868e3	Migration of cluster layout from v0.8 to v0.9	2023-01-11 17:47:46 +01:00
Alex	4f409f73dc	Merge pull request 'Changed all instances of assignation to assignment' (#465 ) from jpds/garage:assignments-correction into next Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/465	2023-01-11 16:05:27 +00:00
Mendes	597d64b31a	change in gitignore	2023-01-09 16:06:47 +01:00
Mendes	e3cc7a89b0	First draft of t a preprint describing the layout computation algorithm	2023-01-09 16:05:20 +01:00
Jonathan Davies	cb07e6145c	Changed all instances of assignation to assignment.	2023-01-05 11:09:25 +00:00
Alex	80e4abb98d	Merge pull request 'Changed all instances of 'key new' to 'key create' to make it the same as the bucket commands.' (#459 ) from jpds/garage:key-create-standardize into next Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/459	2023-01-04 10:35:49 +00:00
Alex Auvolat	570e5e5bbb	Merge branch 'main' into next	2023-01-04 11:34:43 +01:00
Jonathan Davies	8be862aa19	Changed all instances of 'key new' to 'key create' to make it consistent as bucket commands issued normally around the same time.	2023-01-03 11:11:12 +00:00
Alex	6e44369cbc	Merge pull request 'Optimal layout assignation algorithm' (#296 ) from optimal-layout into next Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/296	2022-12-11 17:41:53 +00:00
Alex Auvolat	2c2e65ad8b	Merge commit 'ec12d6c' into next	2022-12-11 18:41:15 +01:00
Alex Auvolat	9d83364ad9	itertools .unique() doesn't require sorted items	2022-12-11 18:30:02 +01:00
Alex Auvolat	ec12d6c8dd	Slightly simplify code at places	2022-11-08 16:15:45 +01:00
Alex Auvolat	217abdca18	Fix HTTP return code	2022-11-08 15:38:53 +01:00
Alex Auvolat	fc2729cd81	Fix integration test	2022-11-08 15:19:46 +01:00
Alex Auvolat	d75b37b018	Return more info when layout's .check() fails, fix compilation, fix test	2022-11-08 14:58:39 +01:00
Alex Auvolat	73a4ca8b15	Use bytes as capacity units	2022-11-07 21:12:11 +01:00
Alex Auvolat	fd5bc142b5	Ensure .sort() is called before counting unique items	2022-11-07 20:29:25 +01:00
Alex Auvolat	ea5afc2511	Style improvements	2022-11-07 20:11:30 +01:00
Alex Auvolat	28d7a49f63	Merge branch 'main' into optimal-layout	2022-11-07 12:20:59 +01:00
Alex Auvolat	3039bb5d43	rm .gitattributes	2022-10-13 12:40:42 +02:00
Mendes	bcdd1e0c33	Added some comment	2022-10-11 18:29:21 +02:00
Mendes	e5664c9822	Improved the statistics displayed in layout show corrected a few bugs	2022-10-11 17:17:13 +02:00
Mendes	4abab246f1	cargo fmt	2022-10-10 17:21:13 +02:00
Mendes	fcf9ac674a	Tests written in layout.rs added staged_parameters to ClusterLayout removed the serde(default) -> will need a migration function	2022-10-10 17:19:25 +02:00
Mendes	911eb17bd9	corrected warnings of cargo clippy	2022-10-06 14:53:57 +02:00
Mendes	9407df60cc	Corrected two bugs: - self.node_id_vec was not properly updated when the previous ring was empty - ClusterLayout::merge was not considering changes in the layout parameters	2022-10-06 12:54:51 +02:00
Mendes	a951b6c452	Added a CLI command to update the parameters for the layout computation (for now, only the zone redundancy)	2022-10-05 16:04:19 +02:00
Mendes	ceac3713d6	modifications in several files to : - have consistent error return types - store the zone redundancy in a Lww - print the error and message in the CLI (TODO: for the server Api, should msg be returned in the body response?)	2022-10-05 15:29:48 +02:00
Mendes	829f815a89	Merge remote-tracking branch 'origin/main' into optimal-layout	2022-10-04 18:14:49 +02:00
Mendes	99f96b9564	deleted zone_redundancy from System struct	2022-10-04 18:09:24 +02:00
Mendes	bd842e1388	Correction of a few bugs in the tests, modification of ClusterLayout::check	2022-09-22 19:30:01 +02:00
Mendes	7f3249a237	New version of the algorithm that calculate the layout. It takes as paramters the replication factor and the zone redundancy, computes the largest partition size reachable with these constraints, and among the possible assignation with this partition size, it computes the one that moves the least number of partitions compared to the previous assignation. This computation uses graph algorithms defined in graph_algo.rs	2022-09-21 14:39:59 +02:00
Mendes	c4adbeed51	Added the section with description proofs of the parametric assignment computation in the optimal layout report	2022-09-10 13:51:12 +02:00
Mendes	d38fb6c250	ignore log files in commit	2022-09-08 12:43:33 +02:00
Mendes	81083dd415	Added a first draft version of the algorithm and analysis for the non-strict mode.	2022-08-19 21:21:41 +02:00
Mendes	7b2c065c82	Merge branch 'optimal-layout' of https://git.deuxfleurs.fr/Deuxfleurs/garage into optimal-layout	2022-07-19 13:30:49 +02:00
Mendes	03e3a1bd15	Added the latex report on the optimal layout algorithm	2022-07-18 22:35:29 +02:00
Alex Auvolat	617f28bfa4	Correct small formatting issue	2022-05-05 14:21:57 +02:00
Mendes	948ff93cf1	Corrected the warnings and errors issued by cargo clippy	2022-05-01 16:05:39 +02:00
Alex Auvolat	3ba2c5b424	updated cargo.lock	2022-05-01 10:11:43 +02:00
Alex Auvolat	2aeaddd5e2	Apply cargo fmt	2022-05-01 09:57:05 +02:00
Alex Auvolat	c1d1646c4d	Change the way new layout assignations are computed. The function now computes an optimal assignation (with respect to partition size) that minimizes the distance to the former assignation, using flow algorithms. This commit was written by Mendes Oulamara <mendes.oulamara@pm.me>	2022-05-01 09:54:19 +02:00