## Diagram: Tree-based Inference Process (Search, Prune, Verify, Infer)
### Overview
The image presents a four-stage algorithmic process for decision-making or inference, visualized as a tree traversal. The process flows from left to right, starting with a broad search, followed by pruning, verification, and finally, quantitative inference of rewards and values.
### Components/Axes
* **Nodes:** Represent states ($S_{x,y}$) and actions/endpoints ($A_z$).
* **Edges:** Represent transitions between states.
* **Annotations:**
* **Red 'X':** Indicates a pruned branch or a failed verification.
* **Green Checkmark:** Indicates a successful verification.
* **$w$:** Weighted reward associated with a transition.
* **$v$:** Quality value associated with a node.
* **END:** Denotes the end of an inference path or a state where $v \geq 0.9$.
### Detailed Analysis
#### 1. Search (Left Panel)
This panel shows the full expansion of the decision tree.
* **Root:** $S_1$ branches into $S_{2,1}$ and $S_{2,2}$.
* **Branch $S_{2,1}$:** Leads to $S_{3,1}$ and $S_{3,2}$.
* $S_{3,1}$ leads to $A_1$ (END) and $S_{4,2}$.
