Let $G$ be a CFG in Chomsky normal form that contains $b$ variables. Show that if $G$ generates some string with a derivation having at least $2^b$ steps, then $L(G)$ is infinite.

Let $G$ be a CFG in Chomsky normal form that contains $b$ variables. Show that if $G$ generates some string with a derivation having at least $2^b$ steps, then $L(G)$ is infinite.

This question is from Sipser(Introduction to the theory of computation)

Let G be a CFG in Chomsky normal form that contains b variables. Show that if G generates some string with a derivation having at least 2b steps, L(G) is infinite.

Let $G$ be a CFG in Chomsky normal form that contains $b$ variables. Show that if $G$ generates some string with a derivation having at least $2^b$ steps, then $L(G)$ is infinite.