The agent programming language Golog features nondeterministic constructs such as nondeterministic branching. Given an optimization theory the nondeterminism can be resolved optimally. There are techniques that allow to derive an abstract first-order description of a value function which is valid across all possible domain instances. The size of the domain may be unknown or even infinite. A finite horizon is assumed, though. That is, although the value function makes no assumptions about the size of the domain, the plans generated on the basis of the value functions are restricted to a certain length. In this paper we present a solution for this dilemma for a specific class of programs. In particular, we present a solution that allows to compute a representation of the value function for non-nested loops without requiring any restrictions on the number of loop iterations. A pleasing side effect is that our new representation of the value function is usually smaller than the representations for fixed horizons.