Abstract
In the first part this paper gives an order-theoretic analysis of the multiset ordering, the recursive path ordering and the lexicographic path ordering with respect to order types and maximal order types. In the second part relativized ordinal notation systems, i. e. “ordinary” ordinal notation systems relativized to a given partial order, are introduced and investigated for the general study of precedence-based termination orderings. It is indicated that (at least) the reduction orderings mentioned above are special cases of this construction.
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References
E. A. Cichon: Bounds on derivation lengths from termination proofs. Technical Report CSD-TR-622, Department of Computer Science, University of London, Surrey, England, June 1990.
J. N. Crossley, J. B. Kister: Natural well-orderings. Archiv für Mathematische Logik und Grundlagenforschung 26 (1986/87), pp. 57–76.
N. Dershowitz, J. P. Jouannaud: Rewrite systems. In: Handbook of Theoretical Computer Science, Part B, Elsevier 1990, pp. 243–320.
N. Dershowitz, M. Okada: Proof theoretic techniques for term rewriting theory. Proceedings of the Third Annual Symposium on Logic in Computer Science, Edinburgh, July 1988, pp. 104–111.
S. Feferman: Proof theory: A personal report. In the appendix of: G. Takeuti: Proof Theory. North-Holland 1987, pp. 447–485.
J. H. Gallier: What's so special about Kruskal's theorem and the ordinal Г0? A survey of some results in proof theory. Annals of Pure and Applied Logic 53 (1991), pp. 199–260.
J. Y. Girard: Introduction to Π 12 -logic. Synthese 62 (1985), pp. 191–216.
L. Gordeev: Generalizations of the Kruskal-Friedman theorems. Journal of Symbolic Logic 55 (1990), pp. 157–181.
L. Gordeev: Systems of iterated projective ordinal notations and combinatorial statements about binary labeled trees. Archive for Mathematical Logic 29 (1989), pp. 29–46.
D. H. J. de Jongh, R. Parikh: Well-partial orderings and hierarchies. Indagationes Math. 39 (1977), pp. 195–207.
C. R. Murthy, J. R. Russell: A constructive proof of Higman's lemma. Proceedings of the Fifth Annual Symposium on Logic and Computer Science, Philadelphia, PA, June 1990, pp. 257–267.
M. Okada, G. Takeuti: On the theory of quasi-ordinal diagrams. Contemporary Mathematics 65, Logic and Combinatorics, Proceedings of the AMS (1987), pp. 295–308.
M. Rathjen: Proof-theoretic analysis of KPM. Archive for Mathematical Logic 30 (1990), pp. 377–403.
K. Schütte: Proof Theory. Springer, 1977.
K. Schütte: Ein Wohlordnungsbeweis für das Ordinalzahlensystem T(J). Archive for Mathematical Logic 27 (1988), pp. 5–20.
D. Schmidt: Well-Partial Orderings and Their Maximal Order Types. Habilitationsschrift, Heidelberg 1979.
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© 1992 Springer-Verlag Berlin Heidelberg
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Weiermann, A. (1992). Proving termination for term rewriting systems. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023786
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DOI: https://doi.org/10.1007/BFb0023786
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