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Dependency Pairs Revisited

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Rewriting Techniques and Applications (RTA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3091))

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Abstract

In this paper we present some new refinements of the dependency pair method for automatically proving the termination of term rewrite systems. These refinements are very easy to implement, increase the power of the method, result in simpler termination proofs, and make the method more efficient.

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References

  1. Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical. Computer Science 236, 133–178 (2000)

    MATH  MathSciNet  Google Scholar 

  2. Arts, T., Giesl, J.: A collection of examples for termination of term rewriting using dependency pairs. Technical Report AIB-2001-09, RWTH Aachen (2001)

    Google Scholar 

  3. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  4. Bachmair, L., Dershowitz, N.: Commutation, transformation, and termination. In: Siekmann, J.H. (ed.) CADE 1986. LNCS, vol. 230, pp. 5–20. Springer, Heidelberg (1986)

    Google Scholar 

  5. Borralleras, C., Ferreira, M., Rubio, A.: Complete monotonic semantic path orderings. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 346–364. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Contejean, E., Marché, C., Monate, B., Urbain, X.: CiME version 2 (2000), Available at http://cime.lri.fr/

  7. Dershowitz, N.: 33 Examples of termination. In: Comon, H., Jouannaud, J.-P. (eds.) TCS School 1993. LNCS, vol. 909, pp. 16–26. Springer, Heidelberg (1995)

    Google Scholar 

  8. Dershowitz, N.: Termination dependencies. In: Proceedings of the 6th International Workshop on Termination, Technical Report DSIC-II/15/03, Universidad Politécnica de Valencia, pp. 27–30 (2003)

    Google Scholar 

  9. Giesl, J., Arts, T., Ohlebusch, E.: Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation 34(1), 21–58 (2002)

    Article  MathSciNet  Google Scholar 

  10. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Improving dependency pairs. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 165–179. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing dependency pairs. Technical Report AIB-2003-08, RWTH Aachen, Germany (2003)

    Google Scholar 

  12. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Automated termination proofs with AProVE. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 210–220. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Gramlich, B.: Generalized sufficient conditions for modular termination of rewriting. Applicable Algebra in Engineering, Communication and Computing 5, 131–158 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 32–46. Springer, Heidelberg (2003) (Full version submitted for publication)

    Chapter  Google Scholar 

  15. Hirokawa, N., Middeldorp, A.: Tsukuba termination tool. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 311–320. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  16. Hirokawa, N., Middeldorp, A.: Tyrolean termination tool (2004), Available at http://cl2-informatik.uibk.ac.at/ttt

  17. Middeldorp, A.: Approximations for strategies and termination. In: Proceedings of the 2nd International Workshop on Reduction Strategies in Rewriting and Programming. Electronic Notes in Theoretical Computer Science, vol. 70(6) (2002)

    Google Scholar 

  18. Middeldorp, A., Ohsaki, H.: Type introduction for equational rewriting. Acta Informatica 36(12), 1007–1029 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  19. Steinbach, J., Kühler, U.: Check your ordering – termination proofs and open problems. Technical Report SR-90-25, Universität Kaiserslautern (1990)

    Google Scholar 

  20. Terese, A.: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  21. Thiemann, R., Giesl, J., Schneider-Kamp, P.: Improved modular termination proofs using dependency pairs. In: Proceedings of the 2nd International Joint Conference on Automated Reasoning, LNCS(LNAI) 2004 (to appear)

    Google Scholar 

  22. Toyama, Y.: Counterexamples to the termination for the direct sum of term rewriting systems. Information Processing Letters 25, 141–143 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  23. Urbain, X.: Modular & incremental automated termination proofs. Journal of Automated Reasoning (2004) (to appear)

    Google Scholar 

  24. Zantema, H.: TORPA: Termination of rewriting proved automatically. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 95–104. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Hirokawa, N., Middeldorp, A. (2004). Dependency Pairs Revisited. In: van Oostrom, V. (eds) Rewriting Techniques and Applications. RTA 2004. Lecture Notes in Computer Science, vol 3091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25979-4_18

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  • DOI: https://doi.org/10.1007/978-3-540-25979-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22153-1

  • Online ISBN: 978-3-540-25979-4

  • eBook Packages: Springer Book Archive

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