  We demonstrate that the greedy algorithm for reduction of divisors on metric
graphs need not terminate by modeling the Euclidean algorithm in this context.
We observe that any infinite reduction has a well defined limit allowing us to
treat the greedy reduction algorithm as a transfinite algorithm and to analyze
its running time via ordinal numbers. We provide lower and upper bounds which
establish a worst case running time of $\omega^{\Theta({\rm deg}(D))}$.
