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Automated Termination Proofs with AProVE

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

Abstract

We describe the system ProVE, an automated prover to verify (innermost) termination of term rewrite systems (TRSs). For this system, we have developed and implemented efficient algorithms based on classical simplification orders, dependency pairs, and the size-change principle. In particular, it contains many new improvements of the dependency pair approach that make automated termination proving more powerful and efficient. In ProVE, termination proofs can be performed with a user-friendly graphical interface and the system is currently among the most powerful termination provers available.

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References

  1. Arts, T.: System description: The dependency pair method. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 261–264. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Arts, T., Giesl, J.: A collection of examples for termination of term rewriting using dependency pairs. Technical Report AIB-2001-093, RWTH Aachen (2001)

    Google Scholar 

  4. 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 

  5. Contejean, E., Marché, C., Monate, B., Urbain, X.: CiME, http://cime.lri.fr

  6. Dershowitz, N.: Termination of rewriting. J. Symb. Comp. 3, 69–116 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  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., Lindenstrauss, N., Sagiv, Y., Serebrenik, A.: A general framework for automatic termination analysis of logic programs. Applicable Algebra in Engineering, Communication and Computing 12(1,2), 117–156 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dick, J., Kalmus, J., Martin, U.: Automating the Knuth-Bendix ordering. Acta Informatica 28, 95–119 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fissore, O., Gnaedig, I., Kirchner, H.: Cariboo: An induction based proof tool for termination with strategies. In: Proc. 4th PPDP, pp. 62–73. ACM, New York (2002)

    Google Scholar 

  11. Giesl, J.: Generating polynomial orderings for termination proofs. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol. 914, pp. 426–431. Springer, Heidelberg (1995)

    Google Scholar 

  12. Giesl, J., Arts, T.: Verification of Erlang processes by dependency pairs. Appl. Algebra in Engineering, Communication and Computing 12(1,2), 39–72 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. 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 

  14. 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 

  15. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing dependency pairs. Technical Report AIB-2003-083, RWTH Aachen, Germany (2003)

    Google Scholar 

  16. Giesl, J., Zantema, H.: Liveness in rewriting. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 321–336. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  17. 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)

    Chapter  Google Scholar 

  18. 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 

  19. Kamin, S., Lévy, J.J.: Two generalizations of the recursive path ordering. Unpublished Manuscript, University of Illinois, IL, USA (1980)

    Google Scholar 

  20. Knuth, D., Bendix, P.: Simple word problems in universal algebras. In: Leech, J. (ed.) Comp. Problems in Abstract Algebra, pp. 263–297. Pergamon, Oxford (1970)

    Google Scholar 

  21. Korovin, K., Voronkov, A.: Verifying orientability of rewrite rules using the knuth-bendix order. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 137–153. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  22. Lankford, D.: On proving term rewriting systems are Noetherian. Technical Report MTP-3, Louisiana Technical University, Ruston, LA, USA (1979)

    Google Scholar 

  23. Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: Proc. POPL 2001, pp. 81–92 (2001)

    Google Scholar 

  24. Ohlebusch, E.: Termination of logic programs: Transformational approaches revisited. Appl. Algebra in Engineering, Comm. and Comp. 12(1,2), 73–116 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  25. Ohlebusch, E., Claves, C., Marché, C.: TALP: A tool for the termination analysis of logic programs. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 270–273. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  26. Steinbach, J.: Automatic termination proofs with transformation orderings. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol. 914, pp. 11–25. Springer, Heidelberg (1995); Full version appeared as Technical Report SR-92-23, Universität Kaiserslautern, Germany

    Google Scholar 

  27. Thiemann, R., Giesl, J.: Size-change termination for term rewriting. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 264–278. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  28. Thiemann, R., Giesl, J., Schneider-Kamp, P.: Improved modular termination proofs using dependency pairs. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 75–90. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  29. Urbain, X.: Automated incremental termination proofs for hierarchically defined term rewriting systems. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 485–498. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  30. 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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Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S. (2004). Automated Termination Proofs with AProVE . 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_15

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  • DOI: https://doi.org/10.1007/978-3-540-25979-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22153-1

  • Online ISBN: 978-3-540-25979-4

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