On two intervals in the lattice of partial ultraclones of rank $2$

In article the intervals in the lattice of partial ultraclones of rank $2$ are considered. The well-known classes of all monotone $M$ and all self-dual $S$ Boolean functions are partial ultraclones of rank $2$. We proved that each of the intervals $\Im (M, M_2)$ and $\Im (S, M_2)$, where $M_2$ is complete partial ultraclone of rank $2$, is finite.