Given an undirected graph, two vertices $s$ and $t$, and two integers $k$ and $r$, then a $k$-set of internally disjoint $s$-$t$-paths is defined to be a set of exactly $k$ $s$-$t$-paths that share no vertex except for $s$ and $t$. What is the complexity of deciding whether there are $r$ pairwise edge-disjoint $k$-sets of internally disjoint $s$-$t$-paths?
It is obviously in $\mathsf{NP}$, but i can neither find a reduction to show $\mathsf{NP}$-hardness, nor a polynomial algorithm.
