Unification under associativity and idempotence is of type nullary

It is shown, that there exist a unification problem〈s=t〉 AI , for which the set of solutions under associativity and idempotence is not empty. But $$\mu U\sum _{Al} \left( {s,t} \right)$$ , the complete and minimal subset of this set of solutions does not exist, i.e.A+I is of type nullary. This is the first known standard first order theory with this unpleasant feature.