Multi-completion with Termination Tools (System Description)

  • Haruhiko Sato
  • Sarah Winkler
  • Masahito Kurihara
  • Aart Middeldorp
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5195)

Abstract

In this paper we describe a new tool for performing Knuth-Bendix completion with automatic termination tools. It is based on two ingredients: (1) the inference system for completion with multiple reduction orderings introduced by Kurihara and Kondo (1999) and (2) the inference system for completion with external termination provers proposed by Wehrman, Stump and Westbrook (2006) and implemented in the Slothrop system. Our tool can be used with any termination tool that satisfies certain minimal requirements. Preliminary experimental results show the potential of our tool.

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References

  1. 1.
    Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: Automatic termination proofs in the dependency pair framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Knuth, D.E., Bendix, P.: Simple word problems in universal algebras. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, Oxford (1970)Google Scholar
  3. 3.
    Kurihara, M., Kondo, H.: Completion for multiple reduction orderings. Journal of Automated Reasoning 23(1), 25–42 (1999)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Sattler-Klein, A.: About changing the ordering during Knuth-Bendix completion. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 175–186. Springer, Heidelberg (1994)Google Scholar
  5. 5.
    Stump, A., Löchner, B.: Knuth-Bendix completion of theories of commuting group endomorphisms. Information Processing Letters 98(5), 195–198 (2006)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Wehrman, I.: Knuth-Bendix completion with modern termination checking. Master’s thesis, Washington University in St. Louis, Technical report WUCSE-2006-45 (2006)Google Scholar
  7. 7.
    Wehrman, I., Stump, A., Westbrook, E.M.: Slothrop: Knuth-Bendix completion with a modern termination checker. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 287–296. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Haruhiko Sato
    • 1
  • Sarah Winkler
    • 2
  • Masahito Kurihara
    • 1
  • Aart Middeldorp
    • 2
  1. 1.Graduate School of Information Science and TechnologyHokkaido UniversityJapan
  2. 2.Institute of Computer ScienceUniversity of InnsbruckAustria

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