Snakes can be fooled into thinking they live in a tree
Abstract
We construct a finitely generated group which is not virtually free, yet has decidable snake tiling problem. This shows that either a long-standing conjecture by Ballier and Stein (the characterization of groups with decidable domino problem as those virtually free ones) is false, or a question by Aubrun and Bitar has a positive answer (there exists a group for which the domino and snake problems are of different difficulty).
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