Simple Definition of a Simple Grammar (with confusing example) This is the definition of simple grammar that I got from the book "Formal Languages and Automata" by Peter Linz.

There is a homework question that asks for a simple grammar for the language L(aaa*b + b).
This is the answer that I found.


I don't see how this could be right, or much less how there could be any answer to this question. If you go S -> aA -> aaBC -> aaaBC ... then you will get infinite a's. The B->aB rule has no possibility of terminating. Is there something I am missing or is the answer to this question just wrong? If it is wrong then is there a possible answer and what is it?
You're right, the grammar is wrong. Everything would be fine, though, if you were able to eventually eliminate the $B$. Here's a way to do that:
$$
S\rightarrow b\mid aA\\
A\rightarrow aB\\
B\rightarrow aB\mid b
$$
The first production generates a singleton $b$ or the first $a$, the second generates the second $a$ and the third eventually generates an arbitrary number of $a$s followed by a $b$.