Let a directed graph D = (V, A) with |V | =: n and |A| =: m, arc capacities u R A 0 , and two nodes s, t V be given. A maximum s-t-preflow in D is a feasible s-t-preflow x R A 0 with ex_x(t) maximal

Show that for a given maximum s-t-preflow x there is a maximum s-t-flow y with ex_y (t) = ex_x(t) and y(a) x(a) for all a A. Hint: Use flow decomposition.