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This is a shortest path problem, albeit of a strange sort.
Although usually we use pathfinding algorithms to find routes through space, where each node in the search space corresponds to a physical location, they actually work just fine on more general graphs too.
In this case, each node in the search space is one snapshot of state the game could be in on ...
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I arrived here by Googling this problem myself, read the linked articles, and produced a relatively compact solution which generates the common set of 47 tiles. It requires a 2x3 tileset for the autotiled material like this:
With a single-tile variant at the top left, inner corners at the top right, and four outer corner tiles at the bottom (you may ...
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