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Journal of Automated Reasoning

, Volume 54, Issue 2, pp 101–133 | Cite as

Labelings for Decreasing Diagrams

  • Harald Zankl
  • Bertram Felgenhauer
  • Aart Middeldorp
Open Access
Article

Abstract

This article 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 article have been implemented and experimental results demonstrate how, e.g., the rule labeling benefits from our contributions.

Keywords

Term rewriting Confluence Decreasing diagrams Automation 

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Copyright information

© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • Harald Zankl
    • 1
  • Bertram Felgenhauer
    • 1
  • Aart Middeldorp
    • 1
  1. 1.Institute of Computer ScienceUniversity of InnsbruckInnsbruckAustria

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