Abstract
The constant-abstraction and variable-abstraction methods for associative-commutative unification were proposed by Herold, Livesey, and Siekmann and by Stickel, respectively. These methods are compared here for efficiency and conceptual purity. The pure variable-abstraction method is easier to implement but less efficient for the variables and constants case than the constant-abstraction method. With obvious refinements, the former method can be made comparably efficient and similar in behavior to the latter. The refined method uses solutions of homogeneous linear Diophantine equations under additional constraints, instead of the conceptually simpler homogeneous or inhomogeneous linear Diophantine equations without additional constraints of the pure variable-abstraction method or the constant-abstraction method.
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