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Decomposing terminating rewrite relations

We decompose an arbitrary rewrite relation into the product of a context-free system and an inverse context-free system with empty right-hand sides. By requiring both of these relations to be terminating, we lose computational completeness and arrive at the class of deleting rewriting systems [5]. Our new treatment allows to efficiently construct the rewrite closure of a regular language with respect to deleting or match-bounded [3] rewriting. Previous implementations of this method either used a complete but inefficient decomposition algorithm [5] leading to impracticable resource consumption, or incomplete approximation algorithms [4]. Our new algorithm is both efficient and exact, thereby improving the power of automated termination provers that use the method of match-bounds.