Standard completion fails whenever an equation s ≈ t is generated, such that s and t are irreducible, yet incomparable with respect to the given reduction ordering. Examples of such unorientable equations are commutativity axioms x · y ≈ y · x, as the two terms x · y and y · x are incomparable with respect to any reduction ordering.
KeywordsInference Rule Critical Pair Horn Clause Ground Term Ground Instance
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