Any ground associative-commutative theory has a finite canonical system

  • Paliath Narendran
  • Michaël Rusinowitch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 488)


We show that theories presented by a set of ground equations with several associative-commutative (AC) symbols always admit a finite canonical system. This result is obtained through the construction of a reduction ordering which is AC-compatible and total on the set of congruence classes generated by the associativity and commutativity axioms. As far as we know, this is the first ordering with such properties, when several AC function symbols and free function symbols are allowed. Such an ordering is also a fundamental tool for deriving complete theorem proving strategies with built-in associative commutative unification.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Paliath Narendran
    • 1
  • Michaël Rusinowitch
    • 2
  1. 1.Inst. of Prog. and Logics SUNY at AlbanyAlbanyUSA
  2. 2.INRIA & CRINVandoeuvre-les-NancyFrance

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