How to simplify this context-free grammar into a similar one with no unit productions and no useless symbols?
$$ S \to ABA \\ A \to aAA \mid aBC \mid bB \\ B \to A \mid bB \mid Cb \\ C \to CC \mid cC $$
Can the simplification result in this CFG?
$$ S \to ABA \\ A \to aAA \\ A \to Bb \\ B \to b $$