Correcting check and adding an explicit explaination of what happens …

…with caching

.github/workflows/test-twostep-container-build.yml

@@ -116,7 +116,7 @@ jobs:
 
       - name: Check the output
         run: |
-          if [ "${{ steps.twostep-2.outputs.summary }}" == "re-built" ]; then
+          if [ "${{ steps.twostep-2.outputs.summary }}" == "rebuilt" ]; then
             echo "Using a re-built version (OK)"
           else
             echo "This was supposed to use the cache version"

twostep-container-build/README.md

@@ -9,6 +9,21 @@ flowchart LR
   Containerfile2-->|Generates|Image2
 ```
 
+The bulk of the action is dealing with whether the first image is available or not. If available, the action will check if the cache key matches the hash of the container file. If it does, the action will skip the first step and use the cached image. If the cache key does not match, the action will build the image and push it to the registry (if `push-image-1` is set to `true`):
+
+```mermaid
+flowchart TB
+  subgraph "Caching"
+    start((Start)) --> tag_exists
+    tag_exists{Tag exists}-->|Yes|pull_image
+    pull_image[Pull image<br>& inspect<br>labels]-->check_label
+    check_label{Label<br>matches<br>hash}-->|Yes|done((Done))
+    check_label-->|No|build_image["Build image<br>& push (optional)"]
+    tag_exists-->|No|build_image
+    build_image-->done
+  end
+```
+
 Caching is done by storing the cache-key as a label in the image (`TWO_STEP_BUILD_CACHE_KEY`); and the build and push process is done using the [docker/build-push-action@v6](https://github.com/docker/build-push-action/tree/v6) action. Users have to explicitly provide the cache key for the first step. For example, if you are dealing with an R package, you can cache the dependencies by passing the key `${{ hashFiles('DESCRIPTION') }}` to the `first-step-cache-key` input. That way, the first step will only be executed if the dependencies change.
 
 ## Inputs and Outputs