Abstract
We show that confluence of shallow and right-linear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems is known to be regularity-preserving, which implies that its reachability and joinability problems are decidable. The new decidability result is obtained by building upon our prior work for the class of ground term rewriting systems and shallow linear term rewriting systems. The proof relies on the concept of extracting more general rewrite derivations from a given rewrite derivation.
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The first author was partially supported by Spanish Min. of Educ. and Science by the LogicTools project (TIN2004-03382). The second author was supported in part by the National Science Foundation under grants ITR-CCR-0326540 and CCR-0311348.
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Godoy, G., Tiwari, A. (2005). Confluence of Shallow Right-Linear Rewrite Systems. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_37
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DOI: https://doi.org/10.1007/11538363_37
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