Modularity in Noncopying Term Rewriting

It is known that termination and completeness are not modular properties of term rewriting systems: the disjoint union of terminating (complete) term rewriting systems need not be terminating (complete). In this paper, we introduce a class of “noncopying” term rewriting systems as a new, term-based formalism for a kind of graph rewriting systems, and prove that this class enjoys the modularity of termination and of completeness. Actually, our results are stronger in the sense that the disjointness condition is relaxed for allowing the systems to share constructors and some defined symbols while preserving the main results.

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