Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 4G / c / Solution

The original grammar generatesbecause each use of $S\to ASc$ adds one $a$ on the left and one $c$ on the right, and $S\to B\to b$ terminates the derivation.

Introduce nonterminals $S_0,X,C$ and useEvery production is in Chomsky normal form. The production $X\to SC$ completes one matched $a,c$ pair, while either start-like symbol terminates with $b$, so the grammar generates exactly the same language. These productions are a valid $G_{\mathrm{Chom}}$.