Given an undirected graph, two vertices $s$ and $t$, and two integers $k$,$l$ - what is the complexity of finding $\ell$ edge-disjoint $s$-$t$-paths such that at least $k$ of them are pairwise internally disjoint? Being internally disjoint means that the paths are vertex disjoint except for $s$ and $t$.
I know that deciding whether there is a certain amount of edge- or vertex disjoint paths can be solved polynomially with max flow algorithms, but this problem seems way harder. I know it is in $\mathsf{NP}$, however i can't figure out whether it is $\mathsf{NP}$-hard... or is there even some polynomial algorithm?
