Simplification of CFG
C isn't Part of the grammar recursion. As it expands to Terminals only, it is artificial in the Sense That it is only used for notational convenience while it is unnecessary for expressing the CFG.

The simplified grammar obviously contains a typo, as no words containing b are derivable contradicting S -&gt; aBC -&gt; abC -&gt; ababb which the original grammar allows.

The first rule should probably read S -&gt; aAa | aBabb.