Skip to main content
SpringerLink
Log in

Termination by completion

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

This paper presents a completion procedure for proving termination of term rewrite systems. It works as follows. Given a term rewrite systemR supposed to terminate and a term rewrite systemT used to transformR, the completion builds an auxiliary term rewrite systemS, the system transformed ofR byT. The termination ofS andT associated with a property called local cooperation implies the termination ofR. If the process terminates this provides a mechanical proof of the termination ofR.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bachmair, L.: Proof by consistency in equational theories. Technical Report, SUNY at Stony Brook USA, 1988

  2. Bachmair, L., Dershowitz, N.: Commutation, transformation and termination. In: Siekmann, J. (ed.) Proceedings 8th Conf. on Automated Deduction, Lecture Notes in Computer Science, vol. 230, pp. 5–20. Berlin, Heidelberg, New York: Springer 1986

    Google Scholar 

  3. Bachmair, L., Dershowitz, N., Hsiang, J.: Orderings for equational proofs. In: Proceedings Symp. Logic in Computer Science. IEEE, 346–357 (1986)

  4. Bellegarde, F.: Rewriting systems onFP expressions to reduce the number of sequences yielded. Sci. Comput. Programming6, 11–34 (1986)

    Google Scholar 

  5. Bellegarde, F.: Utilisation des systèmes de réécriture d'expressions fonctionnelles comme outils de transformation de programmes itératifs. Thèse de doctorat d'Etat, Université de Nancy I, 1985

  6. Bellegarde, F., Lescanne, P.: Termination proofs based on transformation techniques. Internal Report 86-R-034. Centre de Recherche en Informatique de Nancy, 1986

  7. Bellegarde, F., Lescanne, P.: Transformation orderings. In: 12th Coll. on Trees in Algebra and Programming. TAPSOFT. Lecture Notes in Computer Science, vol. 249, pp. 69–80. Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  8. BenCherifa, A., Lescanne, P.: Termination of rewriting systems by polynomial interpretations and its implementation. Sci. Comput. Programming9, 137–160 (1987)

    Google Scholar 

  9. Curien, P.L.: Categorical combinators, sequential algorithms and functional programming. New York: Pitman Press 1986

    Google Scholar 

  10. Dauchet, M.: Simulation of Turing machines by a left-linear rewrite rule. In: Dershowitz, N. (ed.) Proceedings 3rd Conference on Rewriting Techniques and Applications, Chapel Hill. North Carolina, USA. Lecture Notes in Computer Science, vol. 355, pp. 109–120. Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  11. Dershowitz, N.: Orderings for term-rewriting systems. Theoret. Comput. Sci.17, 279–301 (1982)

    Google Scholar 

  12. Dershowitz, N.: Termination of rewriting. J. Symb. Comput.3, 69–116 (1987)

    Google Scholar 

  13. Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: Van Leuven (ed.) Handbook of Theoretical Computer Science. Amsterdam, New York: North-Holland 1990

    Google Scholar 

  14. Galabertier, B.: Implémentation de l'ordre de terminaison par transformation. Technical Report, Centre de Recherche en Informatique de Nancy, 1988

  15. Geser, A.: Relative termination. Dissertation thesis, Universität Passau, West Germany, 1990

    Google Scholar 

  16. Hardin, T., Laville, A.: Proof of termination of the rewriting system SUBST on CCL. Theoret. Comput. Sci.46, 305–312 (1986)

    Google Scholar 

  17. Huet, G.: Confluent reductions: abstract properties and applications to term rewriting systems. J. Assoc. Comput. Machinery27, 797–821 (1980) Preliminary version in 18th Symposium on Foundations of Computer Science, IEEE, 1977

    Google Scholar 

  18. Huet, G., Lankford, D.-S.: On the uniform halting problem for term rewriting systems. Technical Report 283, Laboria, France, 1978

    Google Scholar 

  19. Kamin, S., Lévy, J.-J.: Attemps for generalizing the recursive path ordering. 1980. Unpublished manuscript

  20. Lankford, D.S.: On Proving Term Rewriting Systems are Noetherian. Technical Report, Louisiana Tech. University, Mathematics Department, Ruston LA, 1979

    Google Scholar 

  21. Lescanne, P.: Completion procedures as transition rules + control. In: Diaz, M., Orejas, F. (ed.) TAPSOFT'89. Lecture Notes in Computer Science, Vol. 351, pp. 28–41. Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  22. Plaisted, D.: A recursively defined ordering for proving termination of term rewriting systems. Technical Report R-78-943, University of Illinois, Department of Computer Science, 1978

  23. Rusinowitch, M.: Path of subterms ordering and recursive decomposition ordering revisited. J. Symb. Comput.3, 117–132 (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Western Washington University, 98225, Bellingham, WA, USA

    Françoise Bellegarde

  2. Centre de Recherche en Informatique de Nancy, CNRS and INRIA-Lorraine, Domaine Scientifique Victor Grignard, BP 239, F-54506, Vandœuvre-lès-Nancy, France

    Pierre Lescanne

Authors
  1. Françoise Bellegarde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pierre Lescanne
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bellegarde, F., Lescanne, P. Termination by completion. AAECC 1, 79–96 (1990). https://doi.org/10.1007/BF01810293

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01810293

Keywords

Search

Navigation