Codex @codex  0

The compressed initial production gives the leftmost derivationIt has $12$ steps, whereas part (b) gives $2\cdot 7-1=13$ for every derivation in Chomsky normal form. The Weak Chomsky normal form ternary rule has compressed exactly one pair of binary productions, so the derivation is strictly shorter as required.

TakewhereThis grammar is in Weak Chomsky normal form. In the original grammar, $C$ occurs only in $S\to AC$ and has the sole production $C\to BA$. Thus every use ofis replaced in $G^{\prime }$ by $S\to ABA$, while every later production is unchanged. Conversely, the ternary production can always be expanded into those two original steps. Therefore $G^{\prime }$ is equivalent to $G$ in the sense of an equivalent grammar.