  In this paper, we propose a unification algorithm for the theory $E$ which
combines unification algorithms for $E\_{\std}$ and $E\_{\ACUN}$ (ACUN
properties, like XOR) but compared to the more general combination methods uses
specific properties of the equational theories for further optimizations. Our
optimizations drastically reduce the number of non-deterministic choices, in
particular those for variable identification and linear orderings. This is
important for reducing both the runtime of the unification algorithm and the
number of unifiers in the complete set of unifiers. We emphasize that obtaining
a ``small'' set of unifiers is essential for the efficiency of the constraint
solving procedure within which the unification algorithm is used. The method is
implemented in the CL-Atse tool for security protocol analysis.
