Simulating Dependency Pairs by Semantic Labeling

Authors Teppei Saito , Nao Hirokawa

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Teppei Saito
  • JAIST, Nomi, Japan
Nao Hirokawa
  • JAIST, Nomi, Japan


The second author is grateful to Vincent van Oostrom for his valuable questions and comments on his talk at FSCD 2021. We thank René Thiemann and Jürgen Giesl for telling us about the first correctness proof of the dependency pair method via semantic labeling. Last but certainly not least, Alfons Geser and Aart Middeldorp’s help on literature was indispensable for this work.

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Teppei Saito and Nao Hirokawa. Simulating Dependency Pairs by Semantic Labeling. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


We show that termination proofs by a version of the dependency pair method can be simulated by semantic labeling plus multiset path orders. By incorporating a flattening technique into multiset path orders the simulation result can be extended to the dependency pair method for relative termination, introduced by Iborra et al. This result allows us to improve applicability of their dependency pair method.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
  • Term rewriting
  • Relative termination
  • Semantic labeling
  • Dependency pairs


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