E-unification algorithms for a class of confluent term rewriting systems

Abstract

E-unification is the problem of unification in equational theories. The narrowing mechanism and term rewriting systems constitute a powerful tool for constructing complete and efficient unification algorithms for useful classes of equational theories. This has been shown for the case where term rewriting systems are confluent and noetherian. In this paper we show that extension of the application domain of narrowing to non-terminating term rewriting systems is possible, though difficult. Specifically, we show that the narrowing process, combined with ordinary unification, yields a complete unification algorithm for equational theories that can be described by a closed linear term rewriting system with the non-repetition property; this class allows non-terminating term rewriting systems. For some special forms of input terms, narrowing generates complete sets of E-unifiers without resorting to the non-repetition property.