Abstract
The purpose of this paper is to describe a decision algorithm for unifiability of equations w.r.t. the equational theory D of two distributive axioms: x ∗ (y + z) = x ∗ y + x ∗ z and (x + y)∗z = x∗z + y∗z. The algorithm is described as a set of non-deterministic transformation rules. The equations given as input are eventually transformed into an AC1-unification-problem with linear constant restrictions. Since the algorithm terminates, this is a solution for an open problem in the field of unification and shows decidability of D-unification. One spin-off is an algorithm that decides the word-problem w.r.t. D in polynomial time. This is the basis for an N ℘-algorithm for D-matching, hence D-matching is N ℘-complete. A further (future) spin-off is a decision algorithm for stratified context unification problems.
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