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A Complete Characterization of Termination of 0p 1q→ 1r 0s


We characterize termination of one-rule string rewriting systems of the form 0p 1q→ 1r 0s for every choice of positive integers p, q, r, and s. In doing so we introduce a termination proof method that applies to some hard examples. For the simply terminating cases, i.e. string rewriting systems that can be ordered by a division order, we give the precise complexity of derivation lengths.

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Received: July 31, 1997; revised version: January 30, 2000

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Zantema, H., Geser, A. A Complete Characterization of Termination of 0p 1q→ 1r 0s. AAECC 11, 1–25 (2000).

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  • Keywords: String rewriting, Term rewriting, Termination, Simple termination, Transformation ordering, Dummy elimination, Derivation length.