A modular property of term rewriting systems is one that holds for the direct sum of two disjoint term rewriting systems iff it holds for every involved term rewriting system. A term rewriting system is r-consistent iff there is no term that can be rewritten to two different variables. We show that the subclass of left-linear and r-consistent term rewriting systems has the modular termination p...

A simple method is proposed for testing equivalence in a restricted domain of two given term rewriting systems. By using the Church-Rosser property and the teachability of term rewriting systems, the method allows us to prove equivalence of these systems without the explicit use of induction; this proof usually requires some kind of induction. The method proposed is a general extension of induc...

A property is persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . Zantema showed that termination is persistent for term rewriting systems without collapsing or duplicating rules. In this paper, we show that the Zantema’s result can be extended to term rewriting ...