$4.$ Given the following grammar:

S $->$ AB $|$ aB

A $->$ abb $|$

B $->$ bbA

$($a$)$ Simplify the grammar rules by removing any $-$productions, unit$-$productions, and useless productions.

$($b$)$ Convert the grammar in $($a$)$ into Chomsky normal form.

$($c$)$ Convert the grammar in $($a$)$ into Greibach normal form.