So I got:
$ S \rightarrow XY|a $
$ X \rightarrow XYb|XS|\varepsilon$
$ Y \rightarrow SY|cX|XX|a$
So I want to solve this step by step ( first seperate, avoid length $\geq$ 2, avoid $\varepsilon$, avoid chain rules ).
(i)
$ S \rightarrow XY|a $
$ X \rightarrow XYB|XS|\varepsilon$
$ Y \rightarrow SY|CX|XX|a$
$ B \rightarrow b $
$ C \rightarrow c $
(ii)
$ S \rightarrow XY|a $
$ X \rightarrow XD|XS|\varepsilon$
$ Y \rightarrow SY|CX|XX|a$
$ B \rightarrow b $
$ C \rightarrow c $
$ D \rightarrow YB $
(iii)
$ S \rightarrow XY|X|Y|a $
$ X \rightarrow XD|XS|D|S|X$ is X $\rightarrow$ X necessary ?
$ Y \rightarrow SY|CX|XX|X|Y|S|C|a$ is Y $\rightarrow$ Y necessary ?
$ B \rightarrow b $
$ C \rightarrow c $
$ D \rightarrow YB|B $
(iv) here is my problem. I had to guess at this part
$ S \rightarrow XY|a|XD|XS|YB|b|SY|CX|XX|c $
$ X \rightarrow XD|XS|YB|b|XY|a|SY|CX|XX|c$
$ Y \rightarrow SY|CX|XX|a|c|b|XD|XS|YB|XY$
$ B \rightarrow b $
$ C \rightarrow c $
$ D \rightarrow YB|b $
I know that this is heart to read. Thank you in advance.