Termination Proofs and the Length of Derivations⋆
نویسندگان
چکیده
The derivation height of a term t relative to a set R of rewrite rules, dhR(t), is the length of a longest derivation from t. We investigate in which way certain termination proof methods impose bounds on dhR. In particular we show that if termination of R can be proved by polynomial interpretation then dhR is bounded from above by a doubly exponential function, whereas termination proofs by Knuth–Bendix ordering are possible even for systems where dhR cannot be bounded by any primitive recursive function. For both methods, conditions are given which guarantee a singly exponential upper bound on dhR. Moreover, all upper bounds are tight.
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