Normalized Completion Revisited

Authors Sarah Winkler, Aart Middeldorp

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Sarah Winkler
Aart Middeldorp

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Sarah Winkler and Aart Middeldorp. Normalized Completion Revisited. In 24th International Conference on Rewriting Techniques and Applications (RTA 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 21, pp. 319-334, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


Normalized completion (Marché 1996) is a widely applicable and efficient technique for com- pletion modulo theories. If successful, a normalized completion procedure computes a rewrite system that allows to decide the validity problem using normalized rewriting. In this paper we consider a slightly simplified inference system for finite normalized completion runs. We prove correctness, show faithfulness of critical pair criteria in our setting, and propose a different notion of normalizing pairs. We then show how normalized completion procedures can benefit from AC- termination tools instead of relying on a fixed AC-compatible reduction order. We outline our implementation of this approach in the completion tool mkbtt and present experimental results, including new completions.
  • term rewriting
  • completion


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