figure graphs after two units of flow added along sbdact using correct algorithm there is no augmenting path in this graphso the algorithm terminates note that the same result would occur if at figure the augmenting path sact was chosen which allows one unit of flowbecause then subsequent augmenting path could be found it is easy to see that if the algorithm terminatesthen it must terminate with maximum flow termination implies that there is no path from to in the residual graph so cut the residual graphputting the vertices reachable from on one side and the unreachables (which include ton the other side figure shows the cut clearly any edges in the original graph that cross the cut must be saturatedotherwisethere would be residual flow remaining on one of the edgeswhich would then imply an edge that crosses the cut (in the wrong disallowed directionin gr but that means that the flow in is exactly equal to the capacity of cut in ghencewe have maximum flow if the edge costs in the graph are integersthen the algorithm must terminateeach augmentation adds unit of flowso we eventually reach the maximum flowthough there figure the vertices reachable from in the residual graph form one side of cutthe unreachables form the other side of the cut