  This paper addresses the torsion problem for a class of automaton semigroups,
defined as semigroups of transformations induced by Mealy automata, aka
letter-by-letter transducers with the same input and output alphabet. The
torsion problem is undecidable for automaton semigroups in general, but is
known to be solvable within the well-studied class of (semi)groups generated by
invertible bounded Mealy automata. We focus on the somehow antipodal class of
invertible reversible Mealy automata and prove that for a wide subclass the
generated semigroup is torsion-free.
