The Joinability and Unification Problems for Confluent Semi-constructor TRSs

The unification problem for term rewriting systems (TRSs) is the problem of deciding, for a TRS R and two terms s and t, whether s and t are unifiable modulo R. Mitsuhashi et al. have shown that the problem is decidable for confluent simple TRSs. Here, a TRS is simple if the right-hand side of every rewrite rule is a ground term or a variable. In this paper, we extend this result and show that the unification problem for confluent semi-constructor TRSs is decidable. Here, a semi-constructor TRS is such a TRS that every subterm. of the right-hand side of each rewrite rule is ground if its root is a defined symbol. We first show the decidability of joinability for confluent semi-constructor TRSs. Then, using the decision algorithm for joinability, we obtain a. unification algorithm for confluent semi-constructor TRSs.