# Efficiency/Redundancy in Chomsky normal form

I have a context-free grammar with the following production rules, $$S$$ being the start symbol:

\begin{align*} S &\to AB \\ A &\to a \\ B &\to a\end{align*}

Is this in Chomsky normal form?

My problem is I thought CNF is supposed to be an efficient way to write a grammar, yet the grammar is not efficient in the sense that we can clean its rules as follows:

\begin{align*}S &\to AA\\ A &\to a\end{align*}

Both grammars are in CNF. One of the possible rule formats for CNF is $$A \to BC$$, where $$A$$, $$B$$, and $$C$$ are non-terminals, but it is not necessary for them to be different from another. Hence, in your case, $$S \to AA$$ is also a valid rule for CNF.