Well-foundedness of term orderings

  • M. C. F. Ferreira
  • H. Zantema
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 968)


Well-foundedness is the essential property of orderings for proving termination. We introduce a simple criterion on term orderings such that any term ordering possessing the subterm property and satisfying this criterion is well-founded. The usual path orders fulfil this criterion, yielding a much simpler proof of well-foundedness than the classical proof depending on Kruskal's theorem. Even more, our approach covers non-simplification orders like spo and gpo which can not be dealt with by Kruskal's theorem.

For finite alphabets we present completeness results, i. e., a term rewriting system terminates if and only if it is compatible with an order satisfying the criterion. For infinite alphabets the same completeness results hold for a slightly different criterion.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • M. C. F. Ferreira
    • 1
  • H. Zantema
    • 1
  1. 1.Department of Computer ScienceUtrecht UniversityTB UtrechtThe Netherlands

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