On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup

It is proved that if $\pi$-Hall subgroup is a supersolvable group then the derived $\pi$-length of a $\pi$-solvable group $G$ is at most $1+ \max_{r\in \pi}l_r^a(G),$ where $l_r^a(G)$ is the derived $r$-length of a $\pi$-solvable group $G.$