Labelings for Decreasing Diagrams

Harald Zankl, Bertram Felgenhauer, and Aart Middeldorp

Proceedings of the 22nd International Conference on Rewriting Techniques and Applications (RTA 2011), Leibniz International Proceedings in Informatics 10, pp. 377 – 392, 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 whichsubsumes 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.


  PDF |    doi:10.4230/LIPIcs.RTA.2011.377  |  © Creative Commons License – NC – ND


author = "Harald Zankl and Bertram Felgenhauer and Aart Middeldorp",
title = "Labelings for Decreasing Diagrams",
booktitle = "Proceedings of the 22nd International Conference on Rewriting
Techniques and Applications",
series = "Leibniz International Proceedings in Informatics",
volume = 10,
pages = "377--392",
year = 2011
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