Congruence Closure modulo Associativity-Commutativity
Abstract
We introduce the notion of an associative-commutative congruence closure and show how such closures can be constructed via completion-like transition rules. This method is based on combining completion algorithms for theories over disjoint signatures to produce a convergent system over an extended signature. This approach can also be used to solve the word problem for ground AC-theories without using AC-simplification orderings. We also discuss transformation of a convergent system over an extended signature to a convergent system (modulo AC) over the original signature.