The order types of termination orderings on monadic terms, strings and multisets

U. Martin, E. Scott

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Total well-founded orderings on monadic terms satisfying the replacement and full invariance properties are considered. It is shown that any such ordering on monadic terms in one variable and two unary function symbols must have order type omega , omega /sup 2/, or omega /sup omega /. It is further shown that a familiar construction gives rise to continuum many such orderings of order type omega . A new family of such orderings of order type omega is constructed, and it is shown that there are only four such orderings of order type omega /sup omega /, the two familiar recursive path orderings and two closely related orderings. It is shown that any total well-founded ordering on N/sup n/ that is preserved under vector addition must have order type omega /sup lambda / for some 1>
Original languageEnglish
Title of host publication[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages356-363
Number of pages8
DOIs
Publication statusPublished - 1 Jun 1993

Keywords

  • rewriting systems
  • type theory
  • order types
  • termination orderings
  • monadic terms
  • strings
  • multisets
  • full invariance properties
  • unary function symbols
  • familiar recursive path orderings
  • closely related orderings
  • total well-founded ordering
  • vector addition
  • continuum
  • lexicographic orderings
  • Polynomials

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