Derivation lengths in term rewriting from interpretations in the naturals
نویسنده
چکیده
Monotone interpretations in the natural numbers provide a useful technique for proving termination of term rewriting systems. Termination proofs of this shape imply upper bounds on derivation lengths expressed in bounds on the interpretations. For a hierarchy of classes of interpretations we describe these upper bounds, among which the doubly exponential upper bound for polynomial interpretations, found by Hofbauer and Lautemann. By examples of term rewriting systems we show that all of these upper bounds are sharp in a natural sense. In particular we find all Ackermann functions as sharp upper bounds on derivation lengths, exhausting primitive recursive functions.
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تاریخ انتشار 2017