Abstract
In this paper the Recursive Path Ordering is adapted for proving termination of rewriting incrementally. The new ordering, called Recursive Path Ordering with Modules, has as ingredients not only a precedence but also an underlying ordering \(\sqsupset_{B}\). It can be used for incremental (innermost) termination proofs of hierarchical unions by defining \(\sqsupset_{B}\) as an extension of the termination proof obtained for the base system. Furthermore, there are practical situations in which such proofs can be done modularly.
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References
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236(1-2), 133–178 (2000)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Bendix, P.B., Knuth, D.E.: Simple word problems in universal algebras. In: Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, Oxford (1970)
Borralleras, C.: Ordering-based methods for proving termination automatically. PhD thesis, Dpto. LSI, Universitat Politècnica de Catalunya, España (2003)
Borralleras, C., Ferreira, M., Rubio, A.: Complete monotonic semantic path orderings. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 346–364. Springer, Heidelberg (2000)
Calude, C.: Theories of Computational Complexity. North-Holland, Amsterdam (1988)
Calude, C., Marcus, S., Tevy, I.: The first example of a recursive function which is not primitive recursive. Historia Math. 9, 380–384 (1979)
Dershowitz, N.: Orderings for term rewriting systems. Theoretical Computer Science 17(3), 279–301 (1982)
Fernández, M.L.: Relaxing monotonicity for innermost termination. Information Processing Letters 93(3), 117–123 (2005)
Fernández, M.L.: On proving \(\mathcal{C}\varepsilon\)-termination of rewriting by size-change termination. Information Processing Letters 93(4), 155–162 (2005)
Fernández, M.L., Godoy, G., Rubio, A.: Orderings for innermost termination. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 17–31. Springer, Heidelberg (2005)
Gramlich, B.: On proving termination by innermost termination. In: Ganzinger, H. (ed.) RTA 1996. LNCS, vol. 1103, pp. 93–107. Springer, Heidelberg (1996)
Jouannaud, J.P., Rubio, A.: The higher-order recursive path ordering. In: Proc. LICS, pp. 402–411 (1999)
Krishna Rao, M.R.K.: Modular proofs for completeness of hierarchical term rewriting systems. Theoretical Computer Science 151(2), 487–512 (1995)
Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: Proc. POPL, pp. 81–92 (2001)
Hirokawa, N., Middeldorp, A.: Dependency Pairs Revisited. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 249–268. Springer, Heidelberg (2004)
Ohlebusch, E.: Hierarchical termination revisited. Information Processing Letters 84(4), 207–214 (2002)
Rubio, A.: Extension Orderings. In: Fülöp, Z., Gecseg, F. (eds.) ICALP 1995. LNCS, vol. 944, pp. 511–522. Springer, Heidelberg (1995)
Thiemann, R., Giesl, J.: Size-change termination for term rewriting. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 264–278. Springer, Heidelberg (2003)
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 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, 315–355 (2004)
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Fernández, ML., Godoy, G., Rubio, A. (2005). Recursive Path Orderings Can Also Be Incremental. In: Sutcliffe, G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11591191_17
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DOI: https://doi.org/10.1007/11591191_17
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