$S \rightarrow Aa \ | \ Sa \ | \ c$
$A \rightarrow Ab \ | \ Sd \ | \ e$
First we will remove direct recursion from $S \rightarrow Aa | Sa | c$,
$S \rightarrow AaS' \ | \ cS'$
$S' \rightarrow aS' \ | \ \epsilon $
$A \rightarrow Ab \ | \ Sd \ | \ e$
Then next we can replace productions of $S$ in $A$,
$S \rightarrow AaS' \ | \ cS'$
$S' \rightarrow aS' \ | \ \epsilon $
$A \rightarrow Ab \ | \ AaS'd \ | \ cS'd \ | \ e$
Next we can remove direct recursion from A,
$S \rightarrow AaS' \ | \ cS'$
$S' \rightarrow aS' \ | \ \epsilon $
$A \rightarrow cS'dA' \ | \ eA'$
$A' \rightarrow bA' \ | \ aS'dA' \ | \ \epsilon$