Exercise $31$ Chomsky normal form

Let the context free grammar $G=(\{S,A,B,C,D,E\},\{a,b,c\},P,S)$ be given, where $P$ is defined by

$SAB|A|DCc,BS|ECc,Da|aD$

$AB|CD,C|cC,Eb|bE$

Transform $G$ in a grammar $G^{\text{'}}$ in Chomsky normal form, such that $L(G)=L(G^{\text{'}})$ holds, by applying

the procedure presented in the lecture. Indicate intermediate steps after

removing all $-$productions,

removing all chain productions,

adding new non$-$terminal symbols,

splitting right sides, which are too long.

Submissions without intermediate steps do not achieve any points!

$($In total, there are $20$ points in this exercise sheet.$)$