Using a Ford-Fulkerson algortihm with the restriction that it cannot decrease the flow on an edge, find a flow network with $f>1$ where this algorithm terminates after finding a flow of $ 1 $.
It's pretty easy to find a flow network where the algorithm terminates after finding a suboptimal flow, but is it even possible for it terminate after finding a flow of $ 1 $?
If the first augmenting path picked by the algorithm happens to be S-A-B-T then the algorithm will terminate with a suboptimal flow of 1.
This is because the residual graph will only have edges A-T and S-B since you are not allowed to decrease the flow on an edge.