License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2020.4
URN: urn:nbn:de:0030-drops-123263
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Thiemann, René ; Schöpf, Jonas ; Sternagel, Christian ; Yamada, Akihisa

Certifying the Weighted Path Order (Invited Talk)

LIPIcs-FSCD-2020-4.pdf (0.5 MB)


The weighted path order (WPO) unifies and extends several termination proving techniques that are known in term rewriting. Consequently, the first tool implementing WPO could prove termination of rewrite systems for which all previous tools failed. However, we should not blindly trust such results, since there might be problems with the implementation or the paper proof of WPO.
In this work, we increase the reliability of these automatically generated proofs. To this end, we first formally prove the properties of WPO in Isabelle/HOL, and then develop a verified algorithm to certify termination proofs that are generated by tools using WPO. We also include support for max-polynomial interpretations, an important ingredient in WPO. Here we establish a connection to an existing verified SMT solver. Moreover, we extend the termination tools NaTT and TTT2, so that they can now generate certifiable WPO proofs.

BibTeX - Entry

  author =	{Ren{\'e} Thiemann and Jonas Sch{\"o}pf and Christian Sternagel and Akihisa Yamada},
  title =	{{Certifying the Weighted Path Order (Invited Talk)}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Zena M. Ariola},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-123263},
  doi =		{10.4230/LIPIcs.FSCD.2020.4},
  annote =	{Keywords: certification, Isabelle/HOL, reduction order, termination analysis}

Keywords: certification, Isabelle/HOL, reduction order, termination analysis
Collection: 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)
Issue Date: 2020
Date of publication: 28.06.2020
Supplementary Material: Details on the experiments are provided at This website also provides links to the formalization.

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