Define what it means for a context-free grammar (CFG) to be in Chomsky normal form $(\mathrm{CNF})$.

Describe without proof each stage in the process of converting a CFG $G=$ $(N, \Sigma, P, S)$ into an equivalent CFG $\bar{G}$ which is in CNF. For each of these stages, when are the nonterminals $N$ left unchanged? What about the terminals $\Sigma$ and the generated language $\mathcal{L}(G)$ ?

Give an example of a CFG $G$ whose generated language $\mathcal{L}(G)$ is infinite and equal to $\mathcal{L}(\bar{G})$.