I have the following CFG which I suspect cannot be rewritten to one which is LL(1):
$S \rightarrow \epsilon\ |\ aSbS\ |\ bSaS\ |\ cSdS\ |\ dScS$
I've thought about it for a while, and can't seem to make any progress. I know that the simpler grammar here can be rewritten into LL(1), but it seems like there is something different about the above grammar which prevents a rewriting in a similar style. Is it possible? If not, is there an easy way to prove that this is the case?