AC-Superposition with Constraints: No AC-Unifiers Needed

We prove the completeness of (basic) deduction strategies with constrained clauses modulo associativity and commutativity (AC). Here each inference generates one single conclusion with an additional equality s = AC t in its constraint (instead of one conclusion for each minimal AC-uniier, i.e. exponentially many). Furthermore, computing AC-uniiers is not needed at all. A clause C T ] ] is redundant if the constraint T is not AC-uniiable. If C is the empty clause this has to be decided to know whether C T ] ] denotes an inconsistency. In all other cases any sound method to detect un-satissable constraints can be used.