Abstract
We relate Kamin and Lévy’s original presentation of lexicographic path orders (LPO), using an inductive definition, to a presentation, which we will refer to as iterative lexicographic path orders (ILPO), based on Bergstra and Klop’s definition of recursive path orders by way of an auxiliary term rewriting sytem.
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References
Dershowitz, N.: Orderings for term rewriting systems. TCS 17(3), 279–301 (1982)
Marcone, A.: Fine analysis of the quasi-orderings on the power set. Order 18, 339–347 (2001)
Bergstra, J., Klop, J.: Algebra of communicating processes. TCS 37(1), 171–199 (1985)
Bergstra, J., Klop, J., Middeldorp, A.: Termherschrijfsystemen. In: Programmatuurkunde, Kluwer Academic Publishers, Dordrecht (1989)
Buchholz, W.: Proof-theoretic analysis of termination proofs. APAL 75(1-2), 57–65 (1995)
Kamin, S., Lévy, J.J.: Two generalizations of the recursive path ordering. University of Illinois (1980)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Geser, A.: Relative Termination. PhD thesis, Universität Passau, Germany (1990)
Klop, J.: Term rewriting systems. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic in Computer Science. Background: Computational Structures, vol. 2, pp. 1–116. Oxford University Press, Oxford (1992)
Terese: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55, Cambridge University Press, Cambridge (2003)
Dedekind, R.: Was sind und was sollen die Zahlen?, Brunswick (1888)
Dershowitz, N., Jouannaud, J.P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 243–320. Elsevier, Amsterdam (1990)
Jouannaud, J.P., Rubio, A.: The higher-order recursive path ordering. In: 14th Annual IEEE Symposium on Logic in Computer Science, pp. 402–411. IEEE Computer Society, Los Alamitos (1999)
Bundy, A., Basin, D., Hutter, D., Ireland, A.: Rippling: Meta-Level Guidance for Mathematical Reasoning. Cambridge Tracts in Theoretical Computer Science, vol. 56. Cambridge University Press, Cambridge (2005)
Persson, H.: Type Theory and the Integrated Logic of Programs. PhD thesis, Chalmers, Sweden (1999)
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Klop, J.W., van Oostrom, V., de Vrijer, R. (2006). Iterative Lexicographic Path Orders. In: Futatsugi, K., Jouannaud, JP., Meseguer, J. (eds) Algebra, Meaning, and Computation. Lecture Notes in Computer Science, vol 4060. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780274_28
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DOI: https://doi.org/10.1007/11780274_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35462-8
Online ISBN: 978-3-540-35464-2
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