Skip to main content
SpringerLink
Log in

Combinations of simplifying conditional term rewriting systems

  • Modularity and Termination
  • Conference paper
  • First Online:
Conditional Term Rewriting Systems (CTRS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 656))

Included in the following conference series:

Abstract

A conditional term rewriting system (CTRS) is called simplifying if there exists a simplification ordering > on terms such that the left-hand side of any rewrite rule is greater than the right-hand side and the terms occurring in the conditions of that rule. If a simplifying join CTRS consists of finitely many rules, it is terminating and the applicability of a rewrite rule is decidable by recursively reducing the terms in the conditions. Consider two finite CTRSs R 1 and R 2 which may share constructors (symbols that do not occur at the root position of the lefthand side of any rewrite rule) but no other function symbols. It will be shown that the combined CTRS R = R 1 ∪ R 2 is simplifying if and only if R 1 and R 2 are simplifying. Moreover, confluence is a modular property of finite simplifying join CTRSs.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Dershowitz. Orderings for Term-Rewriting Systems. Theoretical Computer Science 17(3), pages 279–301, 1982.

    Article  Google Scholar 

  2. N. Dershowitz and J.P. Jouannaud. Rewrite Systems. In L. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, chapter 6. North-Holland, 1990.

    Google Scholar 

  3. N. Dershowitz and J.P. Jouannaud. Notations for Rewriting. Bulletin of the EATCS 43, pages 162–172, February 1991.

    Google Scholar 

  4. N. Dershowitz, M. Okada, and G. Sivakumar. Canonical Conditional Rewrite Systems. In Proceedings of the 9th Conference on Automated Deduction, pages 538–549. Lecture Notes in Computer Science 310, Springer Verlag, 1988.

    Google Scholar 

  5. B. Gramlich. A Structural Analysis of Modular Termination of Term Rewriting Systems. SEKI Report SR-91-15, Universität Kaiserslautern, 1991.

    Google Scholar 

  6. S. Kaplan. Simplifying Conditional Term Rewriting Systems: Unification, Termination and Confluence. Journal of Symbolic Computation 4(3), pages 295–334, 1987.

    Google Scholar 

  7. J.W. Klop. Term Rewriting Systems. Report CS-R9073, Centre for Mathematics and Computer Science, 1990.

    Google Scholar 

  8. M. Kurihara and A. Ohuchi. Modularity of Simple Termination of Term Rewriting Systems with Shared Constructors. Report SF-36, Hokkaido University, Sapporo, 1990.

    Google Scholar 

  9. M. Kurihara and A. Ohuchi. Modularity of Simple Termination of Term Rewriting Systems. Journal of IPS Japan 31(5), pages 633–642, 1990.

    Google Scholar 

  10. A. Middeldorp. Confluence of the Disjoint Union of Conditional Term Rewriting Systems. In Proceedings of the 2nd International Workshop on Conditional and Typed Rewriting Systems, pages 295–306. Lecture Notes in Computer Science 516, Springer Verlag, 1990.

    Google Scholar 

  11. A. Middeldorp. Modular Properties of Term Rewriting Systems. PhD thesis, Free University Amsterdam, 1990.

    Google Scholar 

  12. E. Ohlebusch. A Note on Simple Termination of Infinite Term Rewriting Systems. Report Nr. 7, Technische Fakultät, Universität Bielefeld, 1992.

    Google Scholar 

  13. E. Ohlebusch. Combinations of Simplifying Conditional Term Rewriting Systems. Report Nr. 6, Technische Fakultät, Universität Bielefeld, 1992.

    Google Scholar 

  14. M. Rusinowitch. On Termination of the Direct Sum of Term Rewriting Systems. Information Processing Letters 26, pages 65–70, 1987.

    Article  Google Scholar 

  15. J. Steinbach. Extensions and Comparison of Simplification Orderings. In Proceedings of the 3rd International Conference on Rewriting Techniques and Applications, pages 434–448. Lecture Notes in Computer Science 355, Springer Verlag, 1989.

    Google Scholar 

  16. Y. Toyama. Counterexamples to Termination for the Direct Sum of Term Rewriting Systems. Information Processing Letters 25, pages 141–143, 1987.

    Article  Google Scholar 

  17. Y. Toyama. On the Church-Rosser Property for the Direct Sum of Term Rewriting Systems. Journal of the ACM 34(1), pages 128–143, 1987.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität Bielefeld, 4800, Bielefeld 1, Germany

    Enno Ohlebusch

Authors
  1. Enno Ohlebusch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michaël Rusinowitch Jean-Luc Rémy

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ohlebusch, E. (1993). Combinations of simplifying conditional term rewriting systems. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-56393-8_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56393-8

  • Online ISBN: 978-3-540-47549-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation