Every unrestricted grammar there exists an equivalent unrestricted grammar, all of whose productions have the form

$u\rightarrow v,$

with $u,v\in (V \cup T)^+$ and $|u| \leq |v|$, or

$A\rightarrow\lambda$

with $A\in V$

Show that the conclusion still holds if we add the further conditions $|u|\leq2$ and $|v|\leq2$