I went through a question asking me to categorize the following grammar.
$$S → AA, S → AB, A → a, A→BB, B → b, B → e$$
From the production rules, clearly it is Context-Free. But it accepts a finite set of strings. $\{e, a, aa, ab, abb, ba, bba, b, bb, bbb, bbbb\}$ which is regular language.
So, is the above grammar regular? Though it does not follow from the rules.
Basically my question is: Is the grammar $\{S → AA, A → a\}$ regular?.