Complete sets of reductions modulo associativity, commutativity and identity

  • Timothy B. Baird
  • Gerald E Peterson
  • Ralph W. Wilkerson
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 355)


We describe the theory and implementation of a process which finds complete sets of reductions modulo equational theories which contain one or more associative and commutative operators with identity (ACI theories). We emphasize those features which distinguish this process from the similar one which works modulo associativity and commutativity. A primary difference is that for some rules in ACI complete sets, restrictions are required on the substitutions allowed when the rules are applied. Without these restrictions, termination cannot be guaranteed. We exhibit six examples of ACI complete sets that were generated by an implementation.


Equational Theory Unification Algorithm Critical Pair Unification Mechanism Completion Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Timothy B. Baird
    • 1
  • Gerald E Peterson
    • 2
  • Ralph W. Wilkerson
    • 3
  1. 1.Department of Mathematics and Computer ScienceHarding UniversitySearcy
  2. 2.McDonnell Douglas Corporation, W400/105/2/206St. Louis
  3. 3.Department of Computer ScienceUniversity of Missouri—RollaRolla

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