Completeness of combinations of constructor systems

Aart Middeldorp, Yoshihito Toyama

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


A term rewriting system is called complete if it is both confluent and strongly normalising. Barendregt and Klop showed that the disjoint union of complete term rewriting systems does not need to be complete. In other words, completeness is not a modular property of term rewriting systems. Toyama, Klop and Barendregt showed that completeness is a modular property of left-linear term rewriting systems. In this paper we show that it is sufficient to impose the constructor discipline for obtaining the modularity of completeness. This result is a simple consequence of a quite powerful divide and conquer technique for establishing completeness of such constructor systems. Our approach is not limited to systems which are composed of disjoint parts. The importance of our method is that we may decompose a given constructor system into parts which possibly share function symbols and rewrite rules in order to infer completeness. We obtain a similar technique for semi-completeness, i.e. the combination of confluence and weak normalisation.

Original languageEnglish
Pages (from-to)331-348
Number of pages18
JournalJournal of Symbolic Computation
Issue number3
Publication statusPublished - 1993 Mar
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics


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