I'm having trouble to find a language L such that Rank(L)=k AND Rank($L^R$)>$2^{(k+1)}$. (while $L^R$ is L reverse, and Rank is the number of states of the minimal DFA of L by the Myhill–Nerode theorem).
I've been thinking about a language such $L^R$={0}{0,1}$^{(k+1)}$ which has $2^{(k+2)}$ equivalence classes and than see how $L$ looks like, but I couldn't find one that gives me a Rank(L)=k.
is it possible that there is no such language?