This is just a little demo of how the Maze Solver — which just uses the “left-hand rule” explores the entire maze on one side (the left side) of the path. How much of the maze needs to be explored depends on the path. If the path tends to hug the left, the Solver won't have much to explore. If the path hugs right, the Solver can end up exploring much of the maze.
The main point is that the Solver does have to visit every cell on the left side (and none on the right).
|#1 — Maze to be solved.|
|#2 — Solved maze!|