Abstract
The derivation height of a term t, relative to a set R of rewrite rules, dh R (t), is the length of a longest derivation from t. We investigate in which way certain termination proof methods impose bounds on dh R . In particular we show that, if termination of R can be proved by polynomial interpretation then dh R is bounded from above by a doubly exponential function, whereas termination proofs by Knuth-Bendix ordering are possible even for systems where dh R cannot be bounded by any primitive recursive functions. For both methods, conditions are given which guarantee a singly exponential upper bound on dh R . Moreover, all upper bounds are tight.
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in the early stages of this research supported by ESPRIT project PROSPECTRA, ref. #390
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© 1989 Springer-Verlag Berlin Heidelberg
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Hofbauer, D., Lautemann, C. (1989). Termination proofs and the length of derivations. In: Dershowitz, N. (eds) Rewriting Techniques and Applications. RTA 1989. Lecture Notes in Computer Science, vol 355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51081-8_107
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DOI: https://doi.org/10.1007/3-540-51081-8_107
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