Proving Termination by Bounded Increase

  • Jürgen Giesl
  • René Thiemann
  • Stephan Swiderski
  • Peter Schneider-Kamp
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4603)

Abstract

Most methods for termination analysis of term rewrite systems (TRSs) essentially try to find arguments of functions that decrease in recursive calls. However, they fail if the reason for termination is that an argument is increased in recursive calls repeatedly until it reaches a bound. In this paper, we solve that problem and show how to prove innermost termination of TRSs with bounded increase automatically.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236, 133–178 (2000)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge (1998)Google Scholar
  3. 3.
    Brauburger, J., Giesl, J.: Termination analysis by inductive evaluation. In: Kirchner, C., Kirchner, H. (eds.) Automated Deduction - CADE-15. LNCS (LNAI), vol. 1421, pp. 254–269. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Contejean, E., Marché, C., Tomás, A.P., Urbain, X.: Mechanically proving termination using polynomial interpretations. J. Aut. Reason. 34(4), 325–363 (2005)MATHCrossRefGoogle Scholar
  5. 5.
    Cook, B., Podelski, A., Rybalchenko, A.: Terminator: Beyond safety. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 415–418. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Fernández, M.-L.: Relaxing monotonicity for innermost termination. Information Processing Letters 93(3), 117–123 (2005)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Fuhs, C., Giesl, J., Middeldorp, A., Schneider-Kamp, P., Thiemann, R., Zankl, H.: SAT solving for termination analysis with polynomial interpretations. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, Springer, Heidelberg (2007)Google Scholar
  8. 8.
    Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: Combining techniques for automated termination proofs. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 301–331. Springer, Heidelberg (2005)Google Scholar
  9. 9.
    Giesl, J., Thiemann, R., Schneider-Kamp, P.: AProVE 1.2: Automatic termination proofs in the DP framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. Journal of Automated Reasoning 37(3), 155–203 (2006)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Giesl, J., Thiemann, R., Swiderski, S., Schneider-Kamp, P.: Proving termination by bounded increase. Technical Report AIB-2007-03, RWTH Aachen (2007), Available from http://aib.informatik.rwth-aachen.de
  12. 12.
    Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. Information and Computation 199(1,2), 172–199 (2005)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hirokawa, N., Middeldorp, A.: Tyrolean termination tool: Techniques and features. Information and Computation 205(4), 474–511 (2007)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Lankford, D.: On proving term rewriting systems are Noetherian. Technical Report MTP-3, Louisiana Technical University, Ruston, LA, USA (1979)Google Scholar
  15. 15.
    Manolios, P., Vroon, D.: Termination analysis with calling context graphs. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 401–414. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Marché, C., Zantema, H.: The termination competition. In: Proc. RTA  2007 (to appear, 2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jürgen Giesl
    • 1
  • René Thiemann
    • 1
  • Stephan Swiderski
    • 1
  • Peter Schneider-Kamp
    • 1
  1. 1.LuFG Informatik 2, RWTH AachenGermany

Personalised recommendations