Let $G = (V,E)$ be a directed graph with source $s$ and sink $t$ and $s \neq t$. For each edge $e \in E$, we have $c(e) \in \Bbb N$.
also, we are given a max flow function $f$ on that network.
Let $R_f$ be the residual network that represents the max-flow $f$.
I would like to prove that if $R_f$ has a directed cycle with more than 2 edges, then the max flow is not unique (there is more than one max flow).
I tried approaching it in many ways in the last few days but I just get stuck every time when distinguishing between residual edges and edges that also exist in the original network.