Any ground associative-commutative theory has a finite canonical system
Résumé
We show that theories presented by a set of ground equations and with several associative-commutative symbols always admit a finite canonical system. In particular, the 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. Such orderings are fundamental for deriving complete theorem proving strategies with built-in associative commutative unification.