Given the following language, I am tasked with giving a context-free grammar that generates it.
$\left \{ a^{3n}b^{m}c^{n}|n>0, m>0\right \}$
Would this be correct?
$A \rightarrow aaaA$
$B\rightarrow Bb | b$
$C\rightarrow Cc|c$
$S\rightarrow ASBSCS|\epsilon $