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