Modular Properties of Composable Term Rewriting Systems

In this paper we prove several new modularity results for unconditional and conditional term rewriting systems. Most of the known modularity results for the former systems hold for disjoint or constructor-sharing combinations. Here we focus on a more general kind of combination: so-called composable systems. As far as conditional term rewriting systems are concerned, all known modularity result but one apply only to disjoint systems. Here we investigate conditional systems which may share constructors. Furthermore, we refute a conjecture of Middeldorp (1990, 1993).