Termination of context-sensitive rewriting

  • H. Zantema
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1232)


Context-sensitive term rewriting is a kind of term rewriting in which reduction is not allowed inside some fixed arguments of some function symbols. We introduce two new techniques for proving termination of context-sensitive rewriting. The first one is a modification of the technique of interpretation in a well-founded order, the second one is implied by a transformation in which context-sensitive termination of the original system can be concluded from termination of the transformed one. In combination with purely automatic techniques for proving ordinary termination, the latter technique is purely automatic too.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Arts, T., and Giesl, J. Termination of constructor systems. In Proceedings of the 7th Conference on Rewriting Techniques and Applications (1996), vol. 1103 of Lecture Notes in Computer Science, Springer, pp. 63–77.Google Scholar
  2. [2]
    Bellegarde, F., and Lescanne, P. Termination by completion. Applicable Algebra in Engineering, Communication and Computing 1, 2 (1990), 79–96.Google Scholar
  3. [3]
    Ben-Cherifa, A., and Lescanne, P. Termination of rewriting systems by polynomial interpretations and its implementation. Science of Computing Programming 9, 2 (1987), 137–159.Google Scholar
  4. [4]
    Dershowitz, N. Termination of rewriting. Journal of Symbolic Computation 3, 1 and 2 (1987), 69–116.Google Scholar
  5. [5]
    Lucas, S. Fundamentals of context-sensitive rewriting. In Proceedings of the 22nd Seminar on Current Trends in Theory and Practice of Informatics (SOFSEM95) (1995), J. S. M. Bartosek and J. Wiedermann, Eds., vol. 1012 of Lecture Notes in Computer Science, Springer, pp. 405–412.Google Scholar
  6. [6]
    Lucas, S. Context-sensitive computations in confluent programs. In Proceedings of the 8th International Symposium on Programming Languages: Implementations, Logics and Programs (PLILP96) (1996), H. Kuchen and S. D. Swierstra, Eds., vol. 1140 of Lecture Notes in Computer Science, Springer, pp. 403–422.Google Scholar
  7. [7]
    Lucas. S. Termination of context-sensitive rewriting by rewriting. In Proceedings of the 23rd International Colloquium on Automata, Languages and Programming (ICALP96) (1996), F. Meyer auf der Heide and B. Monien, Eds., vol. 1099 of Lecture Notes in Computer Science, Springer, pp. 122–133.Google Scholar
  8. [8]
    Steinbach, J. Simplification orderings: history of results. Fundamenta Informaticae 24 (1995), 47–87.Google Scholar
  9. [9]
    Zantema, H. Termination of term rewriting: interpretation and type elimination. Journal of Symbolic Computation 17 (1994), 23–50.CrossRefGoogle Scholar
  10. [10]
    Zantema, H. Termination of term rewriting by semantic labelling. Fundamenta Informaticae 24 (1995), 89–105.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • H. Zantema
    • 1
  1. 1.Department of Computer ScienceUtrecht UniversityTB UtrechtThe Netherlands

Personalised recommendations