On the Formalization of Termination Techniques based on Multiset Orderings

Authors René Thiemann, Guillaume Allais, Julian Nagele

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René Thiemann
Guillaume Allais
Julian Nagele

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René Thiemann, Guillaume Allais, and Julian Nagele. On the Formalization of Termination Techniques based on Multiset Orderings. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 339-354, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


Multiset orderings are a key ingredient in certain termination techniques like the recursive path ordering and a variant of size-change termination. In order to integrate these techniques in a certifier for termination proofs, we have added them to the Isabelle Formalization of Rewriting. To this end, it was required to extend the existing formalization on multiset orderings towards a generalized multiset ordering. Afterwards, the soundness proofs of both techniques have been established, although only after fixing some definitions. Concerning efficiency, it is known that the search for suitable parameters for both techniques is NP-hard. We show that checking the correct application of the techniques--where all parameters are provided--is also NP-hard, since the problem of deciding the generalized multiset ordering is NP-hard.
  • formalization
  • term rewriting
  • termination
  • orderings


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