Context free grammar to Chomsky's normal form \begin{align*}
S&amp;\to AACD\\
A&amp;\to aAb\\
C&amp;\to aC\mid a\\
D&amp;\to aDa\mid bdb\mid\varepsilon
\end{align*}

I think that this grammar is infinite so it is not possible to convert it into cnf. Am I correct ?
Every context-free grammar can be converted to Chomsky normal form. Also, note that grammars are by definition finite: a grammar might describe infinitely many strings, but the grammar itself is finite.