The torsion problem for a finitely presented group asks whether a given word represents an element of finite order. In this talk, I will present a concrete example of a group with solvable word problem but unsolvable torsion problem. This group is known in the literature as $2V$, and was introduced by Matt Brin in 2004 as a "two-dimensional" version of Thompson's group $V$. As a consequence, I will show that there is no algorithm to determine whether a given asynchronous transducer defines a transformation of finite order. This is joint work with Collin Bleak.