Skip to main content

Nagoya Termination Tool

  • Conference paper
Rewriting and Typed Lambda Calculi (RTA 2014, TLCA 2014)

Abstract

This paper describes the implementation and techniques of the Nagoya Termination Tool, a termination prover for term rewrite systems. The main features of the tool are: the first implementation of the weighted path order which subsumes most of the existing reduction pairs, and the efficiency due to the strong cooperation with external SMT solvers. We present some new ideas that contribute to the efficiency and power of the tool.

This work was supported by JSPS KAKENHI #24500012.

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. TCS 236(1-2), 133–178 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Borralleras, C., Lucas, S., Navarro-Marset, R., Rodríguez-Carbonell, E., Rubio, A.: Solving non-linear polynomial arithmetic via SAT modulo linear arithmetic. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 294–305. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Dershowitz, N.: Orderings for term-rewriting systems. TCS 17(3), 279–301 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  4. Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. JAR 40(2-3), 195–220 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. 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 

  6. 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 

  7. 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)

    Chapter  Google Scholar 

  8. Giesl, J., Thiemann, R., Schneider-Kamp, P.: Proving and disproving termination of higher-order functions. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 216–231. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. JAR 37(3), 155–203 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 249–268. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Hirokawa, N., Middeldorp, A.: Polynomial interpretations with negative coefficients. In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 185–198. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Hirokawa, N., Middeldorp, A., Zankl, H.: Uncurrying for termination and complexity. JAR 50(3), 279–315 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kamin, S., Lévy, J.J.: Two generalizations of the recursive path ordering (1980) (unpublished note)

    Google Scholar 

  14. Knuth, D., Bendix, P.: Simple word problems in universal algebras. In: Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, New York (1970)

    Chapter  Google Scholar 

  15. Lal, A., Qadeer, S., Lahiri, S.K.: A solver for reachability modulo theories. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 427–443. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  16. Lankford, D.: On proving term rewrite systems are Noetherian. Tech. Rep. MTP-3, Louisiana Technical University (1979)

    Google Scholar 

  17. Ludwig, M., Waldmann, U.: An extension of the knuth-bendix ordering with LPO-like properties. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 348–362. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Middeldorp, A., Zantema, H.: Simple termination of rewrite systems. TCS 175(1), 127–158 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. Steinbach, J.: Extensions and comparison of simplification orders. In: Dershowitz, N. (ed.) RTA 1989. LNCS, vol. 355, pp. 434–448. Springer, Heidelberg (1989)

    Google Scholar 

  20. Sternagel, C., Thiemann, R.: Generalized and formalized uncurrying. In: Tinelli, C., Sofronie-Stokkermans, V. (eds.) FroCoS 2011. LNCS, vol. 6989, pp. 243–258. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  21. Winkler, S., Zankl, H., Middeldorp, A.: Ordinals and knuth-bendix orders. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 420–434. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. Xi, H.: Towards automated termination proofs through freezing. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 271–285. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  23. Yamada, A., Kusakari, K., Sakabe, T.: Partial status for KBO. In: Proceedings WST 2013, pp. 74–78 (2013)

    Google Scholar 

  24. Yamada, A., Kusakari, K., Sakabe, T.: Unifying the Knuth-Bendix, recursive path and polynomial orders. In: Proceedings PPDP[15], pp. 181–192 (2013)

    Google Scholar 

  25. Yamada, A., Kusakari, K., Sakabe, T.: Nagoya Termination Tool. CoRR abs/1404.6626 (2014)

    Google Scholar 

  26. Yamada, A., Kusakari, K., Sakabe, T.: A unified order for termination proving. CoRR abs/1404.6245 (2014) (submitted to SCP)

    Google Scholar 

  27. Zankl, H., Hirokawa, N., Middeldorp, A.: KBO orientability. JAR 43(2), 173–201 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Yamada, A., Kusakari, K., Sakabe, T. (2014). Nagoya Termination Tool. In: Dowek, G. (eds) Rewriting and Typed Lambda Calculi. RTA TLCA 2014 2014. Lecture Notes in Computer Science, vol 8560. Springer, Cham. https://doi.org/10.1007/978-3-319-08918-8_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08918-8_32

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08917-1

  • Online ISBN: 978-3-319-08918-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics