A virtual relation (or view) can be defined with a recursive Horn clause that is a function of one or more base relations. In general, the number of times such a Horn clause must be applied in order to retrieve all the tuples in the virtual relation depends on the contents of the base relations of the definition. However, there exist Horn clauses for which there is an upper bound on the number of applications necessary to form the virtual relation, independent of the contents of the base relations. Considering a restricted class of recursive Horn clauses, we give necessary and sufficient conditions for members of the class to have this bound.