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Reducing Relative Termination to Dependency Pair Problems

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Automated Deduction - CADE-25 (CADE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

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Abstract

Relative termination, a generalized notion of termination, has been used in a number of different contexts like proving the confluence of rewrite systems or analyzing the termination of narrowing. In this paper, we introduce a new technique to prove relative termination by reducing it to dependency pair problems. To the best of our knowledge, this is the first significant contribution to Problem #106 of the RTA List of Open Problems. The practical significance of our method is illustrated by means of an experimental evaluation.

Germán Vidal is partially supported by the EU (FEDER) and the Spanish Ministerio de Economía y Competitividad under grant TIN2013-44742-C4-1-R and by the Generalitat Valenciana under grant PROMETEOII2015/013. Akihisa Yamada is supported by the Austrian Science Fund (FWF): Y757.

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Notes

  1. 1.

    Available from URL http://www.termination-portal.org/.

  2. 2.

    http://www.win.tue.nl/rtaloop/.

  3. 3.

    Available at http://www.trs.cm.is.nagoya-u.ac.jp/NaTT/.

  4. 4.

    Details are available at http://www.trs.cm.is.nagoya-u.ac.jp/papers/CADE2015.

  5. 5.

    Available at http://z3.codeplex.com/.

  6. 6.

    Available at http://termination-portal.org/wiki/TPDB.

  7. 7.

    For one of the two problems, the union is terminating.

  8. 8.

    For four examples, AProVE proved relative termination but NaTT failed. There AProVE used semantic labeling [30], which is currently not implemented in NaTT.

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Acknowledgement

We would like to thank Nao Hirokawa and the anonymous reviewers for their helpful comments and suggestions in early stages of this work.

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Authors and Affiliations

  1. Graduate School of Information Science, Nagoya University, Nagoya, Japan

    José Iborra & Naoki Nishida

  2. MiST, DSIC, Universitat Politècnica de València, Valencia, Spain

    Germán Vidal

  3. Institute of Computer Science, University of Innsbruck, Innsbruck, Austria

    Akihisa Yamada

Authors
  1. José Iborra
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  2. Naoki Nishida
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  3. Germán Vidal
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  4. Akihisa Yamada
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Corresponding author

Correspondence to Akihisa Yamada .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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Iborra, J., Nishida, N., Vidal, G., Yamada, A. (2015). Reducing Relative Termination to Dependency Pair Problems. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_11

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_11

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