Q42

Consider the following context-free grammar $G$.

$$\begin{array}{l} S \rightarrow a b a A B A b b a \\ A \rightarrow a a B B A b \mid b B a b a a \\ B \rightarrow a B b \mid a b \end{array}$$

In the above grammar, $S$ is the start symbol, $a$ and $b$ are terminal symbols, and $A$ and $B$ are non-terminal symbols. Let $L(G)$ be the language generated by the grammar $G$. For a string $s \in L(G)$, let $n_{1}(s)$ be the number of $a$ 's in $s$ and $n_{2}(s)$ be the number of $b$ 's in $s$. Which of the following statements is/are true?