Abstract
A semigroup term is a finite word in the alphabet x1, x2,…. The length of a term p, denoted by |p|, is the number of variables in p, including multiplicities. The term-equivalence problem for a finite semigroup S has as an instance a pair of terms {p,q} with size |p| + |q| and asks whether p ≈ q is an identity over S. It is proved here that [Formula: see text], the six-element Perkins semigroup, has co-NP-complete term-equivalence problem, a result which leads to the completion of the classification of he term-equivalence problems for monoid extensions of aperiodic Rees matrix semigroups. From the main result it follows that there exist finite semigroups with tractable term-equivalence problems but having subsemigroups and homomorphic images with co-NP-complete term-equivalence problems.
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