Hydra Battles and AC Termination

Authors Nao Hirokawa , Aart Middeldorp

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Nao Hirokawa
  • School of Information Science, JAIST, Ishikawa, Japan
Aart Middeldorp
  • Department of Computer Science, Universität Innsbruck, Austria

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Nao Hirokawa and Aart Middeldorp. Hydra Battles and AC Termination. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We present a new encoding of the Battle of Hercules and Hydra as a rewrite system with AC symbols. Unlike earlier term rewriting encodings, it faithfully models any strategy of Hercules to beat Hydra. To prove the termination of our encoding, we employ type introduction in connection with many-sorted semantic labeling for AC rewriting and AC-RPO.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
  • Theory of computation → Rewrite systems
  • Theory of computation → Computability
  • battle of Hercules and Hydra
  • term rewriting
  • termination


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