Exercise $7\mathrm{.}1\mathrm{.}8$: Let G be an epsilon$-$production free grammar whose total length of production bodies is n$.$ We convert G to CNF$.$ a$)$ Show that the CNF grammar has at most O$($n$^2)$ productions. b$)$ Show that it is possible for the CNF grammar to have a number of productions proportional to n$^2.$ Hint Consider the construction that eliminates unit productions