Given the Context Free Grammar (CFG) as ({S, A, B, C}, {a, b, c}, R, S) where S is the starting symbol, and the set of rewrite rules R is given as: S rightarrow A | B A rightarrow BAB | BC |B |a | elementof B rightarrow bb| b | elementof C rightarrow CCC | c What is (are) the derivation tree(s) for the string bb, bbabb, and bbbbccc. If there are multiple derivation trees, giving 2 derivation trees suffices. Convert the above grammar into a Chomsky Normal Form. For a context free grammar G given in Chomsky Normal Form, show that the length of string obtained after applying n rewrite rules is at most 2^n. If the number of nonterminals in the grammar is k, show that at least one non-terminal is repeated in the derivation tree of string of length more than 4^k