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Proving non-termination by finite automata

Authors Jörg Endrullis, Hans Zantema

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Jörg Endrullis
Hans Zantema

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Jörg Endrullis and Hans Zantema. Proving non-termination by finite automata. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 160-176, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)


A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies non-termination. Our approach succeeds for many examples where all earlier techniques fail, for instance for the S-rule from combinatory logic.
  • non-termination
  • finite automata
  • regular languages


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