Abstract. Term rewriting systems (TRSs) are extended by allowing to contain extra variables in their rewrite rules. We call the extended systems EV-TRSs. They are ill-natured since every one-step reduction by their rules with extra variables is infinitely branching and they are not terminating. To solve these problems, this paper extends narrowing on TRSs into that on EV-TRSs and show that it simulates the reduction sequences of EV-TRSs as the narrowing sequences starting from ground terms. We prove the soundness of ground narrowing-sequences for the reduction sequences. We prove the completeness for the case of rightlinear systems, and also for the case that no redex in terms substituted for extra variables is reduced in the reduction sequences. Moreover, we give a method to prove the termination of the simulation, extending the termination proof of TRSs using dependency pairs, to that of narrowing on EV-TRSs starting from ground terms.
Nishida, Sakai and Sakabe REF adapted the dependency pair method for proving the termination of narrowing for TRSs with extra variables.
Narrowing-Based Simulation of Term Rewriting Systems with Extra Variables
In Proc. of the 10th ACM SIGPLAN International Conference on Functional Programming (ICFP’05
Computer Science