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 a complete theorem proving strategies with built-in associative commutative unification.
CITATION STYLE
Narendran, P., & Rusinowitch, M. (1991). Any ground associative-commutative theory has a finite canonical system. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 488 LNCS, pp. 423–434). Springer Verlag. https://doi.org/10.1007/3-540-53904-2_115
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