文章基本信息

标题：Automated Confluence Proof by Decreasing Diagrams based on Rule-Labelling
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作者：Takahito Aoto
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2010
卷号：6
页码：7-16
DOI：10.4230/LIPIcs.RTA.2010.7
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Decreasing diagrams technique (van Oostrom, 1994) is a technique that can be widely applied to prove confluence of rewrite systems. To directly apply the decreasing diagrams technique to prove confluence of rewrite systems, rule-labelling heuristic has been proposed by van Oostrom (2008). We show how constraints for ensuring confluence of term rewriting systems constructed based on the rule-labelling heuristic are encoded as linear arithmetic constraints suitable for solving the satisfiability of them by external SMT solvers. We point out an additional constraint omitted in (van Oostrom, 2008) that is needed to guarantee the soundness of confluence proofs based on the rule-labelling heuristic extended to deal with non-right-linear rules. We also present several extensions of the rule-labelling heuristic by which the applicability of the technique is enlarged.
关键词：Confluence; Decreasing Diagrams; Automation; Term Rewriting Systems