  In this paper we investigate the word problem of the free Burnside semigroup
satisfying x^2=x^3 and having two generators. Elements of this semigroup are
classes of equivalent words. A natural way to solve the word problem is to
select a unique "canonical" representative for each equivalence class. We prove
that overlap-free words and so-called almost overlap-free words (this notion is
some generalization of the notion of overlap-free words) can serve as canonical
representatives for corresponding equivalence classes. We show that such a word
in a given class, if any, can be efficiently found. As a result, we construct a
linear-time algorithm that partially solves the word problem for the semigroup
under consideration.
