We know that the generic Ford-Fulkerson Algorithm may not terminate in the presence of irrational capacities and that its maximum bottleneck-capacity variant always terminates within weakly polynomial running time for rational capacities. Is it possible that the augmenting path algorithm does not terminate if we always choose a maximum bottleneck-capacity augmenting path?
(The running time proof for rational capacities shows that in this case the flow value must converge to the maximum flow value.)
Thanks for your time.