I've been struggling a bit with creating the Chomsky normal form derivation of a grammar that I have been given
The grammar in question is:
$S \to BB \mid 0A0 \mid 1B1 \\ A \to C \\ B \to S \mid \varepsilon \\ C \to S \mid A$
So far I have ended up with
$S0 \to S \\ S \to BB \mid 0A0 \mid 1B1 \mid 00 \mid 11 \\ A \to BB \mid 0A0 \mid 1B1 \mid 00 \mid 11 \\ B \to BB \mid 0A0 \mid 1B1 \mid 00 \mid 11 \\ C \to BB \mid 0A0 \mid 1B1 \mid 00 \mid 11$
I assume i am doing something horribly wrong, when doing eliminating unit transitions; would anybody be able to give me a clear explanation of the steps taken?
Thank you!