Abstract
The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. In this paper, we show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different techniques can be combined and their modularity and power are increased significantly. We[2] refer to this new concept as the “dependency pair framework” to distinguish it from the old “dependency pair approach”. Moreover, this framework facilitates the development of new methods for termination analysis. To demonstrate this, we present several new techniques within the dependency pair framework which simplify termination problems considerably. We implemented the dependency pair framework in our termination prover AProVE and evaluated it on large collections of examples.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236, 133–178 (2000)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Dershowitz, N.: Termination of rewriting. J. Symb. Computation 3, 69–116 (1987)
Dershowitz, N.: Termination by abstraction. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 1–18. Springer, Heidelberg (2004)
Geser, A., Hofbauer, D., Waldmann, J.: Match-bounded string rewriting systems. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 449–459. Springer, Heidelberg (2003)
Giesl, J., Arts, T.: Verification of Erlang processes by dependency pairs. Appl. Algebra in Engineering, Communication and Computing 12(1,2), 39–72 (2001)
Giesl, J., Arts, T., Ohlebusch, E.: Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation 34(1), 21–58 (2002)
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)
Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Automated termination proofs with AProVE. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 210–220. Springer, Heidelberg (2004)
Gramlich, B.: Abstract relations between restricted termination and confluence properties of rewrite systems. Fundamenta Informaticae 24, 3–23 (1995)
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); Full version to appear in Information and Computation
Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 249–268. Springer, Heidelberg (2004)
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)
Kamin, S., Lévy, J.J.: Two generalizations of the recursive path ordering. Unpublished Manuscript, University of Illinois, IL, USA (1980)
Knuth, D., Bendix, P.: Simple word problems in universal algebras. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263–297 (1970)
Kusakari, K., Nakamura, M., Toyama, Y.: Argument filtering transformation. In: Nadathur, G. (ed.) PPDP 1999. LNCS, vol. 1702, pp. 48–62. Springer, Heidelberg (1999)
Lankford, D.: On proving term rewriting systems are Noetherian. Technical Report MTP-3, Louisiana Technical University, Ruston, LA, USA (1979)
Middeldorp, A.: A simple proof to a result of Bernhard Gramlich. Presented at the 5th Japanese Term Rewriting Meeting, Tsukuba (1994), Available from http://informatik.uibk.ac.at/users/ami/research/papers/bg.pdf
Steinbach, J.: Simplification orderings: History of results. Fundamenta Informaticae 24, 47–87 (1995)
Termination Problem Data Base (TPDB), Available from http://www.lri.fr/~marche/wst2004-competition/tpdb.html
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)
Toyama, Y.: Counterexamples to the termination for the direct sum of term rewriting systems. Information Processing Letters 25, 141–143 (1987)
Urbain, X.: Modular and incremental automated termination proofs. Journal of Automated Reasoning 32(4), 315–355 (2004)
Zantema, H.: Termination of term rewriting by semantic labelling. Fundamenta Informaticae 24, 89–105 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giesl, J., Thiemann, R., Schneider-Kamp, P. (2005). The Dependency Pair Framework: Combining Techniques for Automated Termination Proofs. In: Baader, F., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32275-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-32275-7_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25236-8
Online ISBN: 978-3-540-32275-7
eBook Packages: Computer ScienceComputer Science (R0)