On the Modularity of Confluence of Constructor-Sharing Term Rewriting Systems

Toyama's Theorem states that connuence is a modular property of disjoint term rewriting systems. This theorem does not generalize to combined systems with shared constructors. Thus the question arises naturally whether there are suucient conditions which ensure the modu-larity of connuence in the presence of shared constructors. In particular, Kurihara and Krishna Rao posed the problem whether there are interesting suucient conditions independent of termination. This question appeared as Problem 59 in the list of open problems in the theory of rewriting published recently DJK93]. The present paper gives an af-rmative answer to that question. Among other suucient criteria, it is shown that connuence is preserved under the combination of constructor-sharing systems if the systems are also normalizing. This in conjunction with the fact that normalization is modular for those systems implies the modularity of semi-completeness.