Containment and reduction for cherry-unresolved reticulated-cherry stack CPNs

Let $N$ and $N'$ be CPNs on the same leaf-set in the $(, )$ class. Here, a cherry-picking sequence (CPS) of $N$ is a sequence used to reduce $N'$, and $N'$ is contained in $N$ according to the network-containment relation. Containment–reduction conjecture. There exist CPNs $N$ and $N'$ on the same leaf-set in this class such that $N'$ is contained in $N$, but no CPS of $N$ reduces $N'$. The converse of the implication that a CPS reducing $N'$ implies containment is known to fail for other reconstructible classes; the corresponding question for this class is stated as open in the source.