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Numerous confluence criteria for plain term rewrite systems are known. Forlogically constrained rewrite system, an attractive extension of term rewritingin which rules are equipped with logical constraints, much less is known. Inthis paper we extend the strongly-closed and (almost) parallel-closed criticalpair criteria of Huet and Toyama to the logically constrained setting. Wediscuss the challenges for automation and present crest, a new tool forlogically constrained rewriting in which the confluence criteria areimplemented, together with experimental data.

Confluence Criteria for Logically Constrained Rewrite Systems (Full Version)