On the Equivalence of Persistent Term Rewriting Systems and Recursive Program Schemes

We introduce Persistent Term Rewriting Systems (PTRSs) by restricting redex-creation during reductions in Orthogonal Term Rewriting Systems (OTRSs [6, 10]). In particular, Recursive (Applicative) Program Schemes (RPSs [4]), considered as TRSs, are persistent. Two PTRSs R and R' are syntactically equivalent when any term t has an R-normal form iff it has an R'-normal form and they coincide. We prove that syntactic equivalence is decidable for PTRSs. Further, we show that the equivalence problem (over all continuous interpretations) is decidable for RPSs with unary basic functions by reducing the question to a decidable number-theory problem. Finally, we show that weak and strong normalization and the reducibility problem also are decidable in PTRSs