Skip to main content
SpringerLink
Log in
Book cover

International Conference on Rewriting Techniques and Applications

RTA 1993: Rewriting Techniques and Applications pp 198–212Cite as

Topics in termination

  • Conference paper

  • 199 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 690))

Abstract

We generalize the various path orderings and the conditions under which they work, and describe an implementation of this general ordering. We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's.

This research was supported in part by the U. S. National Science Foundation under Grants CCR-90-07195 and CCR-90-24271. The first author was also supported by a Lady Davis fellowship at the Hebrew University of Jerusalem.

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

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. Ahlem Ben Cherifa and Pierre Lescanne. Termination of rewriting systems by polynomial interpretations and its implementation. Science of Computer Programming, 9:137–159, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  2. Robert M. Burstall. Proving properties of programs by structural induction. Computing J., 12(1):41–48, February 1969.

    Article  MATH  Google Scholar 

  3. Paul J. Cohen. Decision procedures for real and p-adic fields. Comm. Pure and Applied Math, 22(2): 279–301, March 1969.

    Article  Google Scholar 

  4. Nachum Dershowitz. Termination of linear rewriting systems. In Proceedings of the Eighth International Colloquium on Automata, Languages and Programming, pages 448–458, Acre, Israel, July 1981. European Association of Theoretical Computer Science. Vol. 115 of Lecture Notes in Computer Science, Springer-Verlag, Berlin.

    Google Scholar 

  5. Nachum Dershowitz. Orderings for term-rewriting systems. Theoretical Computer Science, 17(3):279–301, March 1982.

    Article  MATH  MathSciNet  Google Scholar 

  6. Nachum Dershowitz. Termination of rewriting. J. of Symbolic Computation, 3(1&2):69–115, February/April 1987. Corrigendum: 4, 3 (December 1987), 409–410.

    Article  MATH  MathSciNet  Google Scholar 

  7. Nachum Dershowitz. Hierarchical termination. Technical Report, Leibnitz Center for Research in Computer Science, Hebrew University, Jerusalem, Israel.

    Google Scholar 

  8. Nachum Dershowitz and Zohar Manna. Proving termination with multiset orderings. Communications of the ACM, 22(8):465–476, August 1979.

    Article  MATH  MathSciNet  Google Scholar 

  9. Oliver Geupel. Overlap closures and termination of term rewriting systems. Report MIP-8922, Universität Passau, Passau, West Germany, July 1989.

    Google Scholar 

  10. Bernhard Gramlich. Relating innermost, weak, uniform and modular termination of term rewriting systems. Proceedings of the Conference on Logic Programming and Automated Reasoning, pp. 285–296, St. Petersburg, Russia, July 1992. Vol. 624 of Lecture Notes in Computer Science, Springer-Verlag, Berlin.

    Google Scholar 

  11. Sam Kamin and Jean-Jacques Lévy. Two generalizations of the recursive path ordering. Unpublished note, Department of Computer Science, University of Illinois, Urbana, IL, February 1980.

    Google Scholar 

  12. Donald E. Knuth and P. B. Bendix. Simple word problems in universal algebras. In J. Leech, editor, Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, Oxford, U. K., 1970.

    Chapter  Google Scholar 

  13. Dallas S. Lankford. On proving term rewriting systems are Noetherian. Memo MTP-3, Mathematics Department, Louisiana Tech. University, Ruston, LA, October 1979.

    Google Scholar 

  14. Pierre Lescanne. On the recursive decomposition ordering with lexicographical status and other related orderings. J. Automated Reasoning, 6:39–49, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  15. R. Lipton and L. Snyder. On the halting of tree replacement systems. In Proceedings of the Conference on Theoretical Computer Science, pp. 43–46, Waterloo, Canada, August 1977.

    Google Scholar 

  16. Zohar Manna. Mathematical Theory of Computation. McGraw-Hill, New York, 1974.

    MATH  Google Scholar 

  17. Zohar Manna and Steven Ness. On the termination of Markov algorithms. In Proceedings of the Third Hawaii International Conference on System Science, pp. 789–792, Honolulu, HI, January 1970.

    Google Scholar 

  18. Michael J. O'Donnell. Computing in systems described by equations, volume 58 of Lecture Notes in Computer Science. Springer, Berlin, West Germany, 1977.

    Google Scholar 

  19. David A. Plaisted. Well-founded orderings for proving termination of systems of rewrite rules. Report R-78-932, Department of Computer Science, University of Illinois, Urbana, IL, July 1978.

    Google Scholar 

  20. David A. Plaisted. Personal communication, 1979.

    Google Scholar 

  21. Joachim Steinbach and Michael Zehnter. Vade-mecum of polynomial orderings. Report SR-90-03, Fachbereich Informatik, Universität Kaiserslautern, Kaiserslautern, West Germany, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois, 61801, Urbana, IL, USA

    Nachum Dershowitz & Charles Hoot

Authors
  1. Nachum Dershowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Charles Hoot
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. INRIA Lorraine and CRIN, 615 Rue du Jardin Botanique, F-54602, Villers les Nancy Cedex, France

    Claude Kirchner

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dershowitz, N., Hoot, C. (1993). Topics in termination. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-21551-7_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56868-1

  • Online ISBN: 978-3-662-21551-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation