The Unification Problem for One Relation Thue Systems

. We give an algorithm for the unification problem for a generalization of Thue Systems with one relation. The word problem is a special case. We show that in many cases this is a decision procedure with at most an exponential time bound. We conjecture that this is always a decision procedure. 1 Introduction In this paper we study the unification problem and word problem for Thue Systems. This basic problem appears under several di#erent names. It is also known as the unification and word problem for semigroups, terms with monadic function symbols, and ground terms with one associative operator. In particular, we are interested in Thue Systems with only one equation, but we have generalized our results to larger classes. The word problem for one equation can be stated simply: Given an equation s = t, and two words u 0 and un , is there a sequence of words u 0 , ,u n such that each u i+1 is the result of replacing an occurrence of s in u i by t, or replacing an occurrence of t in u ..