Skip to main content

Proving Termination of Integer Term Rewriting

  • Conference paper
Rewriting Techniques and Applications (RTA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5595))

Included in the following conference series:

Abstract

When using rewrite techniques for termination analysis of programs, a main problem are pre-defined data types like integers. We extend term rewriting by built-in integers and adapt the dependency pair framework to prove termination of integer term rewriting automatically.

Supported by the DFG grant GI 274/5-2 and by the G.I.F. grant 966-116.6.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Bradley, A.R., Manna, Z., Sipma, H.B.: Termination of polynomial programs. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 113–129. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Bradley, A.R., Manna, Z., Sipma, H.B.: Linear ranking with reachability. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 491–504. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Chawdhary, A., Cook, B., Gulwani, S., Sagiv, M., Yang, H.: Ranking abstractions. In: Drossopoulou, S. (ed.) ESOP 2008. LNCS, vol. 4960, pp. 148–162. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Colón, M., Sipma, H.B.: Synthesis of linear ranking functions. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 67–81. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Colón, M., Sipma, H.B.: Practical methods for proving program termination. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 442–454. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Cook, B., Podelski, A., Rybalchenko, A.: Abstraction refinement for termination. In: Hankin, C., Siveroni, I. (eds.) SAS 2005. LNCS, vol. 3672, pp. 87–101. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Cook, B., Podelski, A., Rybalchenko, A.: Termination proofs for systems code. In: Proc. PLDI 2006, pp. 415–426. ACM Press, New York (2006)

    Google Scholar 

  9. Falke, S., Kapur, D.: Dependency pairs for rewriting with built-in numbers and semantic data structures. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 94–109. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. 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, pp. 340–354. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Fuhs, C., Giesl, J., Middeldorp, A., Schneider-Kamp, P., Thiemann, R., Zankl, H.: Maximal termination. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 110–125. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. 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  MATH  Google Scholar 

  13. Giesl, J., Thiemann, R., Schneider-Kamp, P.: The DP 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)

    Chapter  Google Scholar 

  14. Giesl, J., Swiderski, S., Schneider-Kamp, P., Thiemann, R.: Automated termination analysis for Haskell: From term rewriting to programming languages. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 297–312. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: Automatic termination proofs in the DP framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS, vol. 4130, pp. 281–286. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. Journal of Automated Reasoning 37(3), 155–203 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Giesl, J., Thiemann, R., Swiderski, S., Schneider-Kamp, P.: Proving termination by bounded increase. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 443–459. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Gulwani, S., Tiwari, A.: Constraint-based approach for analysis of hybrid systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 190–203. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. Information and Computation 199(1,2), 172–199 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hirokawa, N., Middeldorp, A.: Tyrolean Termination Tool: Techniques and features. Information and Computation 205(4), 474–511 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hong, H., Jakuš, D.: Testing positiveness of polynomials. Journal of Automated Reasoning 21(1), 23–38 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  22. Korp, M., Sternagel, C., Zankl, H., Middeldorp, A.: Tyrolean Termination Tool 2. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 295–304. Springer, Heidelberg (2009)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Podelski, A., Rybalchenko, A.: A complete method for the synthesis of linear ranking functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 239–251. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  25. Podelski, A., Rybalchenko, A.: Transition invariants. In: LICS 2004, pp. 32–41 (2004)

    Google Scholar 

  26. Rubio, A.: Present and future of proving termination of rewriting. Invited talk, www.risc.uni-linz.ac.at/about/conferences/rta2008/slides/Slides_Rubio.pdf

  27. Schneider-Kamp, P., Giesl, J., Serebrenik, A., Thiemann, R.: Automated termination proofs for logic programs by term rewriting. ACM Transactions on Computational Logic (to appear, 2009)

    Google Scholar 

  28. Serebrenik, A., De Schreye, D.: Inference of termination conditions for numerical loops in Prolog. Theory and Practice of Logic Programming 4(5,6), 719–751 (2004)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fuhs, C., Giesl, J., Plücker, M., Schneider-Kamp, P., Falke, S. (2009). Proving Termination of Integer Term Rewriting. In: Treinen, R. (eds) Rewriting Techniques and Applications. RTA 2009. Lecture Notes in Computer Science, vol 5595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02348-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02348-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02347-7

  • Online ISBN: 978-3-642-02348-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics