# This is a question about the push-down machine

Suppose $$G$$ is a $$CFG$$ with m variables and not right side of production longer than $$l$$. Show that if $$A\Rightarrow^*_G\varepsilon$$, then there is a derivation of no more than $$\frac{l^m-1}{l-1}$$ steps by which $$A$$ derives $$\varepsilon$$. How close to this bound can you actually come?