Abstract
A rewriting system can be shown terminating by an order-preserving mapping into a well-founded domain. We present an instance of this scheme for string rewriting where the domain is a set of square matrices of natural numbers, equipped with a well-founded ordering that is not total. The coefficients of the matrices can be found via a transformation to a boolean satisfiability problem. The matrix method also supports relative termination, thus it fits with the dependency pair method as well. Our implementation is able to automatically solve hard termination problems.
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References
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoret. Comput. Sci. 236, 133–178 (2000)
Book, R.V., Otto, F.: String-Rewriting Systems. Texts Monogr. Comput. Sci. Springer, New York (1993)
Endrullis, J.: Jambox: Automated termination proofs for string rewriting, http://joerg.endrullis.de/
Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 574–588. Springer, Heidelberg (2006)
Fuchs, L.: Partially Ordered Algebraic Systems. Pergamon Press, Oxford (1963)
Dershowitz, N., Treinen, R.: The RTA list of open problems, http://www.lsv.ens-cachan.fr/rtaloop/
Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)
Geser, A.: Relative Termination. Dissertation, Universität Passau, Germany (1990)
Geser, A., Hofbauer, D., Waldmann, J.: Match-bounded string rewriting systems. Appl. Algebra Engrg. Comm. Comput. 15(3-4), 149–171 (2004)
Hofbauer, D., Waldmann, J.: Termination of { aa →bc, bb →ac, cc →ab }. Inform. Process. Lett. 98, 156–158 (2006)
Kanel-Below, A., Rowen, L.H.: Computational Aspects of Polynomial Identities. A.K. Peters, Wellesley (2005)
The Termination Problems Data Base, Version 2.0 (2005), http://www.lri.fr/~marche/tpdb/
Waldmann, J.: Matchbox: a tool for match-bounded string rewriting. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 85–94. Springer, Heidelberg (2004)
Waldmann, J.: Weighted automata for proving termination of string rewriting. In: Droste, M., Vogler, H. (eds.) Proc. Weighted Automata: Theory and Applications, Leipzig (2006)
Zantema, H.: Termination. In: Terese (ed.) Term Rewriting Systems, pp. 181–259. Cambridge Univ. Press, Cambridge (2003)
Zantema, H.: TORPA: Termination of Rewriting Proved Automatically. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 95–104. Springer, Heidelberg (2004)
Zantema, H.: Problem #104. In: [6] (2005), http://www.lsv.ens-cachan.fr/rtaloop/problems/104.html
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Hofbauer, D., Waldmann, J. (2006). Termination of String Rewriting with Matrix Interpretations. In: Pfenning, F. (eds) Term Rewriting and Applications. RTA 2006. Lecture Notes in Computer Science, vol 4098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11805618_25
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DOI: https://doi.org/10.1007/11805618_25
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