Skip to main content
SpringerLink
Log in
Book cover

International Conference on Automated Deduction

CADE 2003: Automated Deduction – CADE-19 pp 32–46Cite as

Automating the Dependency Pair Method

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2741))

Abstract

Developing automatable methods for proving termination of term rewrite systems that resist traditional techniques based on simplification orders has become an active research area in the past few years. The dependency pair method of Arts and Giesl is one of the most popular such methods. However, there are several obstacles that hamper its automation. In this paper we present new ideas to overcome these obstacles. We provide ample numerical data supporting our ideas.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arts, T.: System description: The dependency pair method. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 261–264. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. TCS 236, 133–178 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Arts, T., Giesl, J.: A collection of examples for termination of term rewriting using dependency pairs. Technical Report AIB-2001-09, RWTH Aachen (2001)

    Google Scholar 

  4. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  5. Bellegarde, F., Lescanne, P.: Termination by completion. AAECC 1, 79–96 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Borralleras, C., Ferreira, M., Rubio, A.: Complete monotonic semantic path orderings. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 346–364. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Contejean, E., Marché, C., Monate, B., Urbain, X.: CiME version 2 (2000), Available at http://cime.lri.fr/

  8. Dershowitz, N.: 33 Examples of termination. In: Comon, H., Jouannaud, J.-P. (eds.) TCS School 1993. LNCS, vol. 909, pp. 16–26. Springer, Heidelberg (1995)

    Google Scholar 

  9. Giesl, J., Arts, T.: Verification of Erlang processes by dependency pairs. AAECC 12(1,2), 39–72 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Giesl, J., Arts, T., Ohlebusch, E.: Modular termination proofs for rewriting using dependency pairs. JSC 34(1), 21–58 (2002)

    MathSciNet  Google Scholar 

  11. Hirokawa, N., Middeldorp, A.: Tsukuba termination tool. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Kamin, S., Lévy, J.J.: Two generalizations of the recursive path ordering. University of Illinois (1980) (unpublished manuscript)

    Google Scholar 

  13. Middeldorp, A.: Approximating dependency graphs using tree automata techniques. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 593–610. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Middeldorp, A.: Approximations for strategies and termination. In: Proc. 2nd WRS. ENTCS, vol. 70(6) (2002)

    Google Scholar 

  15. Steinbach, J.: Automatic termination proofs with transformation orderings. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol. 914, pp. 11–25. Springer, Heidelberg (1995)

    Google Scholar 

  16. Steinbach, J., Kühler, U.: Check your ordering – termination proofs and open problems. Technical Report SR-90-25, Universität Kaiserslautern (1990)

    Google Scholar 

  17. Toyama, Y.: Counterexamples to the termination for the direct sum of term rewriting systems. Information Processing Letters 25, 141–143 (1987)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, 305-8573, Japan

    Nao Hirokawa

  2. Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, 305-8573, Japan

    Aart Middeldorp

Authors
  1. Nao Hirokawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aart Middeldorp
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Germany

    Franz Baader

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hirokawa, N., Middeldorp, A. (2003). Automating the Dependency Pair Method. In: Baader, F. (eds) Automated Deduction – CADE-19. CADE 2003. Lecture Notes in Computer Science(), vol 2741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45085-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45085-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40559-7

  • Online ISBN: 978-3-540-45085-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation