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Termination of Term Rewriting: Foundation, Formalization, Implementation, and Competition (Invited Talk)

Author Akihisa Yamada

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Akihisa Yamada
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

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Akihisa Yamada. Termination of Term Rewriting: Foundation, Formalization, Implementation, and Competition (Invited Talk). In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 4:1-4:5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


Automated termination analysis is a central topic in the research of term rewriting. In this talk, I will first review the theoretical foundation of termination of term rewriting, leading to the recently established tuple interpretation method. Then I will present an Isabelle/HOL formalization of the theory. Although the formalization is based on the existing library IsaFoR (Isabelle Formalization of Rewriting), the present work takes another approach of representing relations (predicates rather than sets) so that the notation is more human friendly. Then I will present a unified implementation of the termination analysis techniques via SMT encoding, leading to the termination prover NaTT. Many tools have been developed for termination analysis and have been competing annually in termCOMP (Termination Competition) for two decades. At the end of the talk, I will share my experience in organizing termCOMP in the last five years.

Subject Classification

ACM Subject Classification
  • Theory of computation → Rewrite systems
  • Theory of computation → Automated reasoning
  • Term rewriting
  • Termination
  • Isabelle/HOL
  • Competition


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