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International Conference on Rewriting Techniques and Applications

RTA 1995: Rewriting Techniques and Applications pp 426–431Cite as

Generating polynomial orderings for termination proofs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 914))

Abstract

Most systems for the automation of termination proofs using polynomial orderings are only semi-automatic, i.e. the “right” polynomial ordering has to be given by the user. We show that a variation of Lank-ford's partial derivative technique leads to an easier and slightly more powerful method than most other semi-automatic approaches. Based on this technique we develop a method for the automated synthesis of a suited polynomial ordering.

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References

  1. F. Bellegarde. Rewriting Systems on FP Expressions that reduce the Number of Sequences they yield. Symp. LISP & Funct. Prog., ACM, Austin, TX, 1984.

    Google Scholar 

  2. A. Ben Cherifa & P. Lescanne. Termination of Rewriting Systems by Polynomial Interpretations and its Implementation. Science of Computer Programming, 9(2):137–159, 1987.

    Article  Google Scholar 

  3. G. E. Collins. Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In Proc. 2nd GI Conf. on Automata Theory and Formal Languages, Kaiserslautern, Germany, 1975.

    Google Scholar 

  4. N. Dershowitz. Orderings for Term-Rewriting Systems. Theoretical Computer Science, 17:279–301, 1982.

    Article  Google Scholar 

  5. N. Dershowitz. Termination of Rewriting. Journal of Symbolic Computation, 3(1, 2):69–115, 1987.

    Google Scholar 

  6. N. Dershowitz & J.-P. Joannaud. Rewrite Systems. Handbook of Theoretical Comp. Science, J. van Leuwen, Ed., vol. B, ch. 6, 243–320, Elsevier, 1990.

    Google Scholar 

  7. G. Huet & D. S. Lankford. On the Uniform Halting Problem for Term Rewriting Systems. Rapport Laboria 283, Institut de Recherche d'Informatique et d'Automatique, Le Chesnay, France, 1978.

    Google Scholar 

  8. D. S. Lankford. A Finite Termination Algorithm. Internal Memo, Southwestern University, Georgetown, TX, 1976.

    Google Scholar 

  9. D. S. Lankford. On Proving Term Rewriting Systems are Noetherian. Technical Report Memo MTP-3, Louisiana Tech. Univ., Ruston, LA, 1979.

    Google Scholar 

  10. J. Steinbach. Termination Proofs of Rewriting Systems — Heuristics for Generating Polynomial Orderings. SEKI-Report SR-91-14, Univ. Kaiserslautern, Germany, 1991.

    Google Scholar 

  11. J. Steinbach. Proving Polynomials Positive. In Proc. 12th Conf. Foundations Software Technology & Theoretical Comp. Sc., New Delhi, India, 1992.

    Google Scholar 

  12. A. Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, Berkeley, 1951.

    Google Scholar 

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Authors and Affiliations

  1. FB Informatik, Technische Hochschule Darmstadt, Alexanderstr. 10, 64283, Darmstadt, Germany

    Jürgen Giesl

Authors
  1. Jürgen Giesl
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Jieh Hsiang

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© 1995 Springer-Verlag Berlin Heidelberg

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Giesl, J. (1995). Generating polynomial orderings for termination proofs. In: Hsiang, J. (eds) Rewriting Techniques and Applications. RTA 1995. Lecture Notes in Computer Science, vol 914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59200-8_77

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  • DOI: https://doi.org/10.1007/3-540-59200-8_77

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59200-6

  • Online ISBN: 978-3-540-49223-8

  • eBook Packages: Springer Book Archive

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