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

  • Hans Zantema
  • Alfons Geser


We characterize termination of one-rule string rewriting systems of the form 0 p 1 q → 1 r 0 s 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.

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


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hans Zantema
    • 1
  • Alfons Geser
    • 2
  1. 1.Universiteit Utrecht, P.O. Box 80089, 3508 Utrecht, The Netherlands (e-mail:
  2. 2.Alte Strasse 42, 94034 Passau, Germany (e-mail:

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