Consider the grammar $G=(\{S,A,B\},\{0,1\},P,S)$, where $P$ consists:
$S\to AB$
$A\to BSB$
$A\to BB$
$B\to 0A1$
$B\to 0$
$A\to 1$
$B\to e$
Find equivalent grammar for which S does not appear on the right of any productions and $S\to e$ is the only production with e on the right.
This is a problem from Formal languages and their relation to automata, 4.16.
I tried to figure out what is L(G), but it was complicated. Then, I made grammar $G'=(\{S,A,B,C\},\{0,1\},P',S)$, where $P'$:
$S\to AB$
$A\to BCB$
$C\to AB$
$A\to BB$
$B\to 0A1$
$B\to 0$
$A\to 1$
but problem is to convert $B\to e$ in corresponding form.