Article

Proving Termination by Bounded Increase

Authors:

René Thiemann,

Stephan Swiderski,

Peter Schneider-KampAuthors Info & Claims

CADE-21: Proceedings of the 21st international conference on Automated Deduction: Automated Deduction

Pages 443 - 459

https://doi.org/10.1007/978-3-540-73595-3_33

Published: 17 July 2007 Publication History

Abstract

Most methods for termination analysis of term rewrite systems (TRSs) essentially try to find arguments of functions that <em>decrease</em>in recursive calls. However, they fail if the reason for termination is that an argument is <em>increased</em>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.

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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).

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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).

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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

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Cited By

Giesl JAschermann CBrockschmidt MEmmes FFrohn FFuhs CHensel JOtto CPlücker MSchneider-Kamp PStröder TSwiderski SThiemann R(2017)Analyzing Program Termination and Complexity Automatically with AProVEJournal of Automated Reasoning10.1007/s10817-016-9388-y58:1(3-31)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1007/s10817-016-9388-y
Thiemann R(2013)Formalizing bounded increaseProceedings of the 4th international conference on Interactive Theorem Proving10.1007/978-3-642-39634-2_19(245-260)Online publication date: 22-Jul-2013
https://dl.acm.org/doi/10.1007/978-3-642-39634-2_19
Sakata TNishida NSakabe T(2011)On proving termination of constrained term rewrite systems by eliminating edges from dependency graphsProceedings of the 20th international conference on Functional and constraint logic programming10.5555/2032603.2032616(138-155)Online publication date: 19-Jul-2011
https://dl.acm.org/doi/10.5555/2032603.2032616
Show More Cited By

Proving Termination by Bounded Increase
1. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms

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Published In

cover image Guide Proceedings

CADE-21: Proceedings of the 21st international conference on Automated Deduction: Automated Deduction

July 2007

520 pages

ISBN:9783540735946

Editor:
Frank Pfenning

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 17 July 2007

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Cited By

Giesl JAschermann CBrockschmidt MEmmes FFrohn FFuhs CHensel JOtto CPlücker MSchneider-Kamp PStröder TSwiderski SThiemann R(2017)Analyzing Program Termination and Complexity Automatically with AProVEJournal of Automated Reasoning10.1007/s10817-016-9388-y58:1(3-31)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1007/s10817-016-9388-y
Thiemann R(2013)Formalizing bounded increaseProceedings of the 4th international conference on Interactive Theorem Proving10.1007/978-3-642-39634-2_19(245-260)Online publication date: 22-Jul-2013
https://dl.acm.org/doi/10.1007/978-3-642-39634-2_19
Sakata TNishida NSakabe T(2011)On proving termination of constrained term rewrite systems by eliminating edges from dependency graphsProceedings of the 20th international conference on Functional and constraint logic programming10.5555/2032603.2032616(138-155)Online publication date: 19-Jul-2011
https://dl.acm.org/doi/10.5555/2032603.2032616
Nguyen MDe schreye DGiesl JSchneider-kamp P(2011)PolytoolTheory and Practice of Logic Programming10.1017/S147106841000002511:1(33-63)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.1017/S1471068410000025
Koprowski AWaldmann J(2009)Max/plus tree automata for termination of term rewritingActa Cybernetica10.5555/1774732.177473819:2(357-392)Online publication date: 1-Feb-2009
https://dl.acm.org/doi/10.5555/1774732.1774738

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