Recall the problem of computing a minimum-cost arborescence in a directed graph G = (V, E)...

Recall the problem of computing a minimum-cost arborescence in a directed graph G = (V, E), with a cost ce ≥ 0 on each edge. Here we will consider the case in which G is a directed acyclic graph—that is, it contains no directed cycles.

As in general directed graphs, there can be many distinct minimum-cost solutions. Suppose we are given a directed acyclic graph G = (V, E), and an arborescence  with the guarantee that for every e ε A, e belongs to some minimum-cost arborescence in G. Can we conclude that A itself must be a minimum-cost arborescence in G? Give a proof or a counterexample with explanation.

Figure: An instance of the zero-skew problem, described in Exercise