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International audienceAsymmetric unification is a new paradigm for unification modulo theories  that introduces irreducibility constraintson one side of a unification problem.  It has important applications in symbolic cryptographic protocol analysis, for which itis often necessary to put irreducibility constraints on portions of a state.  However many facets of asymmetricunification thatare of particular interest, includingits behavior under combinations of disjoint theories, remain poorly understood.In this paper we give a new formulation of the method for unificationin the combination of disjoint equational theories developed by Baader and Schulz that bothgives additional insights into the disjoint combination problem in general, and furthermore allowsus to extend the method to asymmetric unification, giving the first unification method for asymmetric unification in the combination of disjoint theories

On Asymmetric Unification and the Combination Problem in Disjoint Theories