Skip to main content

Termination for the direct sum of left-linear term rewriting systems

Preliminary draft

  • Regular Papers
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 355))

Abstract

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that two term rewriting systems both are left-linear and complete if and only if the direct sum of these systems is so.

This paper is an abbreviated version of the IEICE technical report COMP88-30, July 1988. Now we are preparing a final version for submission based on this draft.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Huet and D. C. Oppen, Equations and rewrite rules: a survey, in: R. Book, ed., Formal languages: perspectives and open problems (Academic Press, 1980) 349–393.

    Google Scholar 

  2. N. Dershowitz. Termination of linear rewriting systems: Preliminary version, Lecture Notes in Comput. Sci. 115 (Springer-Verlag, 1981) 448–458.

    Google Scholar 

  3. H. Ganzinger and R. Giegerich, A note on termination in combinations of heterogeneous term rewriting systems, EATCS Bulletin 31 (1987) 22–28.

    Google Scholar 

  4. J. W. Klop and H. P. Barendregt, Private communication (January 19, 1986).

    Google Scholar 

  5. A. Middeldorp, A sufficient condition for the termination of the direct sum of term rewriting systems, Preliminary Draft, Report IR-150, Free University, Amsterdam (1988).

    Google Scholar 

  6. A. Middeldorp, Modular aspects of properties of term rewriting systems related to normal forms, Preliminary Draft, Free University, Amsterdam (September 1988).

    Google Scholar 

  7. M. Rusinowitch, On termination of the direct sum of term rewriting systems, Inform. Process. Lett. 26 (1987) 65–70.

    Google Scholar 

  8. Y. Toyama, On the Church-Rosser property for the direct sum of term rewriting systems, J. ACM 34 (1987) 128–143.

    Google Scholar 

  9. Y. Toyama, Counterexamples to termination for the direct sum of term rewriting systems, Inform. Process. Lett. 25 (1987) 141–143.

    Google Scholar 

  10. Y. Toyama, Commutativity of term rewriting systems, in: K. Fuchi and L. Kott, eds., Programming of Future Generation Computer II (Norht Holland 1988) 393–407.

    Google Scholar 

  11. Y. Toyama, J.W. Klop, H.P. Barendregt, Termination for the direct sum of left-linear term rewriting systems: Preliminary draft, IEICE technical report COM88-30 (July 1988) 47–55.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Nachum Dershowitz

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Toyama, Y., Klop, J.W., Barendregt, H.P. (1989). Termination for the direct sum of left-linear term rewriting systems. In: Dershowitz, N. (eds) Rewriting Techniques and Applications. RTA 1989. Lecture Notes in Computer Science, vol 355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51081-8_127

Download citation

  • DOI: https://doi.org/10.1007/3-540-51081-8_127

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51081-9

  • Online ISBN: 978-3-540-46149-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics