Automating the dependency pair method

Information and Computation

Volumn 199, Issue 1-2, 2005, Pages 172-199

  Hirokawa, Nao ^a   Middeldorp, Aart ^a  

^a UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

Dependency pair method; Term rewriting; Termination

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; AUTOMATION; GRAPH THEORY; POLYNOMIALS; RECURSIVE FUNCTIONS;

DEPENDENCY PAIR METHODS; KNUTH-BENDIX ORDER; TERM REWRITING; TERMINATION;

AUTOMATA THEORY;

EID: 20144367873     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ic.2004.10.004     Document Type: Conference Paper

References (26)

1. T. Arts, System description: the dependency pair method, in: Proceedings of the 11th International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science, vol. 1833, 2000, pp. 261-264
2. T. Arts, J. Giesl, A Collection of Examples for Termination of Term Rewriting Using Dependency Pairs, Technical Report AIB-2001-09, RWTH Aachen, 2001
3. T. Arts, and J. Giesl Termination of term rewriting using dependency pairs Theoretical Computer Science 236 2000 133 178
4. F. Baader, and T. Nipkow Term Rewriting and All That 1998 Cambridge University Press Cambridge
5. F. Bellegarde, and P. Lescanne Termination by completion Applicable Algebra in Engineering, Communication and Computing 1 1990 79 96
6. C. Borralleras, M. Ferreira, A. Rubio, Complete monotonic semantic path orderings, in: Proceedings of the 17th International Conference on Automated Deduction, Lecture Notes in Artificial Intelligence, vol. 1831, 2000, pp. 346-364
7. E. Contejean, C. Marché, B. Monate, X. Urbain, CiME version 2. 2000. Available at 〈 http://cime.lri.fr/〉
8. N. Dershowitz, 33 Examples of termination, in: French Spring School of Theoretical Computer Science, Lecture Notes in Computer Science, vol. 909, 1995, pp. 16-26
9. J. Giesl, and T. Arts Verification of Erlang processes by dependency pairs Applicable Algebra in Engineering, Communication and Computing 12 1,2 2001 39 72
10. J. Giesl, T. Arts, and E. Ohlebusch Modular termination proofs for rewriting using dependency pairs Journal of Symbolic Computation 34 1 2002 21 58
11. J. Giesl, and A. Middeldorp Transformation techniques for context-sensitive rewrite systems Journal of Functional Programming 14 2004 329 427
12. J. Giesl, R. Thiemann, P. Schneider-Kamp, S. Falke, Improving dependency pairs, in: Proceedings of the 10th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Lecture Notes in Artificial Intelligence, vol. 2850, 2003, pp. 165-179
13. B. Gramlich Abstract relations between restricted termination and confluence properties of rewrite systems Fundamenta Informaticae 24 1995 3 23
14. N. Hirokawa, A. Middeldorp, Dependency pairs revisited, in: Proceedings of the 16th International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science, vol. 3091, 2004, pp. 249-268
15. N. Hirokawa, A. Middeldorp, Polynomial interpretations with negative coefficients, in: Proceedings of the 7th International Conference on Artificial Intelligence and Symbolic Computation, Lecture Notes in Artificial Intelligence, vol. 3249, 2004, 185-198
16. N. Hirokawa, A. Middeldorp, Tsukuba termination tool, in: Proceedings of the 14th International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science, vol. 2706, 2003, pp. 311-320
17. S. Kamin, and J. Lévy, Two Generalizations of the Recursive Path Ordering, Unpublished manuscript, University of Illinois, 1980
18. S. Lucas Context-sensitive rewriting strategies Information and Computation 178 1 2002 294 343
19. A. Middeldorp, Approximating dependency graphs using tree automata techniques, in: Proceedings of the International Joint Conference on Automated Reasoning, Lecture Notes in Artificial Intelligence, vol. 2083, 2001, pp. 593-610
20. A. Middeldorp, Approximations for strategies and termination, in: Proceedings of the 2nd International Workshop on Reduction Strategies in Rewriting and Programming, Electronic Notes in Computer Science, Vol. 70(6), 2002
21. E. Ohlebusch Hierarchical termination revisited Information Processing Letters 84 4 2002 207 214
22. J. Steinbach, Automatic termination proofs with transformation orderings, in: Proceedings of the 6th International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science, vol. 914, 1995, pp. 11-25
23. J. Steinbach, U. Kühler, Check Your Ordering-Termination Proofs and Open Problems, Technical Report SR-90-25, Universität Kaiserslautern, 1990
24. R. Thiemann, J. Giesl, P. Schneider-Kamp, Improved modular termination proofs using dependency pairs, in: Proceedings of the 2nd International Joint Conference on Automated Reasoning, Lecture Notes in Artificial Intelligence, vol. 3097, 2004, pp. 75-90
25. Y. Toyama Counterexamples to the termination for the direct sum of term rewriting systems Information Processing Letters 25 1987 141 143
26. X. Urbain, Modular and incremental automated termination proofs, Journal of Automated Reasoning (2005) (to appear)