Labelings for Decreasing Diagrams

Authors Harald Zankl, Bertram Felgenhauer, Aart Middeldorp

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Harald Zankl
Bertram Felgenhauer
Aart Middeldorp

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Harald Zankl, Bertram Felgenhauer, and Aart Middeldorp. Labelings for Decreasing Diagrams. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 377-392, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


This paper is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local diagrams decreasing. This approach has two immediate benefits. First, it allows to use labelings for linear rewrite systems also for left-linear ones, provided some mild conditions are satisfied. Second, it admits an incremental method for proving confluence which subsumes recent developments in automating decreasing diagrams. The techniques proposed in the paper have been implemented and experimental results demonstrate how, e.g., the rule labeling benefits from our contributions.
  • term rewriting
  • confluence
  • decreasing diagrams
  • labeling


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