Relative undecidability in term rewriting: I. the termination Hierarchy

  • Authors:

  • Alfons Geser;Aart Middeldorp;Enno Ohlebusch;Hans Zantema

  • Affiliations:

  • ICASE, Mail Stop 132C, NASA Langley Research Center, Hampton, Virginia;Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Japan;Faculty of Technology, University of Bielefeld, P.O. Box 10 01 31, Bielefeld, Germany;Department of Computing Science, Eindhoven University of Technology, P.O. Box 513, MB Eindhoven, The Netherlands

  • Venue:
  • Information and Computation
  • Year:
  • 2002

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Abstract

For a hierarchy of properties of term rewriting systems related to termination we prove relative undecidability: For implications X → Y in the hierarchy the property X is undecidable for term rewriting systems satisfying Y. For most implications we obtain this result for term rewriting systems consisting of a single rewrite rule.