Skip to main content
SpringerLink
Log in

Cdiprover3: A Tool for Proving Derivational Complexities of Term Rewriting Systems

  • Conference paper
Interfaces: Explorations in Logic, Language and Computation (ESSLLI 2008, ESSLLI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6211))

  • 481 Accesses

Abstract

This paper describes cdiprover3, a tool for proving termination of term rewrite systems by polynomial interpretations and context dependent interpretations. The methods used by cdiprover3 induce small bounds on the derivational complexity of the considered system. We explain the tool in detail, and give an overview of the employed proof methods.

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

Access this chapter

Log in via an institution
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

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.

Similar content being viewed by others

References

  1. Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theor. Comp. Sci. 236(1,2), 133–178 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Avanzini, M., Moser, G.: Complexity analysis by rewriting. In: Garrigue, J., Hermenegildo, M.V. (eds.) FLOPS 2008. LNCS, vol. 4989, pp. 130–146. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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

    Google Scholar 

  4. Bonfante, G., Cichon, A., Marion, J.Y., Touzet, H.: Algorithms with polynomial interpretation termination proof. J. Funct. Program. 11(1), 33–53 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bonfante, G., Marion, J.Y., Péchoux, R.: Quasi-interpretation synthesis by decomposition. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) ICTAC 2007. LNCS, vol. 4711, pp. 410–424. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Contejean, E., Marché, C., Tomás, A.P., Urbain, X.: Mechanically proving termination using polynomial interpretations. J. Autom. Reason. 34(4), 325–363 (2005)

    Article  MATH  Google Scholar 

  7. Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. J. Autom. Reason. 40(3), 195–220 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. 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 

  9. 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 

  10. Hirokawa, N., Moser, G.: Automated complexity analysis based on the dependency pair method. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 364–379. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Hirokawa, N., Moser, G.: Complexity, graphs, and the dependency pair method. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 652–666. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. Hofbauer, D.: Termination proofs by context-dependent interpretations. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 108–121. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Hofbauer, D., Lautemann, C.: Termination proofs and the length of derivations. In: Dershowitz, N. (ed.) RTA 1989. LNCS, vol. 355, pp. 167–177. Springer, Heidelberg (1989)

    Google Scholar 

  14. Koprowski, A., Waldmann, J.: Arctic termination ... below zero. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 202–216. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Lankford, D.: On proving term-rewriting systems are noetherian. Tech. Rep. MTP-2, Math. Dept., Louisiana Tech. University (1979)

    Google Scholar 

  16. Lescanne, P.: Termination of rewrite systems by elementary interpretations. Formal Aspects of Computing 7(1), 77–90 (1995)

    Article  MATH  Google Scholar 

  17. Marion, J.Y.: Analysing the implicit complexity of programs. Inf. Comput. 183(1), 2–18 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Moser, G., Schnabl, A.: Proving quadratic derivational complexities using context dependent interpretations. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 276–290. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Moser, G., Schnabl, A.: The derivational complexity induced by the dependency pair method. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 255–269. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  20. Moser, G., Schnabl, A., Waldmann, J.: Complexity analysis of term rewriting based on matrix and context dependent interpretations. In: Hariharan, R., Mukund, M., Vinay, V. (eds.) FSTTCS 2008. LIPIcs, vol. 2, pp. 304–315. Schloss Dagstuhl - Leibniz- Zentrum fuer Informatik (2008)

    Google Scholar 

  21. Schnabl, A.: Context Dependent Interpretations, Master’s thesis, Universität Innsbruck (2007), http://cl-informatik.uibk.ac.at/~aschnabl/

  22. Steinbach, J.: Proving polynomials positive. In: Shyamasundar, R.K. (ed.) FSTTCS 1992. LNCS, vol. 652, pp. 191–202. Springer, Heidelberg (1992)

    Google Scholar 

  23. Sternagel, C., Middeldorp, A.: Root-labeling. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 336–350. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  24. TeReSe: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  25. Zantema, H.: Reducing right-hand sides for termination. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 173–197. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, Austria

    Andreas Schnabl

Authors
  1. Andreas Schnabl
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Stanford University, Stanford,, CA, USA

    Thomas Icard

  2. Tilburg University, Tilburg, The Netherlands

    Reinhard Muskens

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schnabl, A. (2010). Cdiprover3: A Tool for Proving Derivational Complexities of Term Rewriting Systems. In: Icard, T., Muskens, R. (eds) Interfaces: Explorations in Logic, Language and Computation. ESSLLI ESSLLI 2008 2009. Lecture Notes in Computer Science(), vol 6211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14729-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14729-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14728-9

  • Online ISBN: 978-3-642-14729-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation