One that can be implemented with PDA (with the help of one stack), will be CFL.
$L_1=\{a^mb^nc^kd^l\, |\, if(m=n)then(k=l)\}$
$L_1$ is CFL , if no of $a's$ = no of $b's$ then we need to ensure no of $c's$ = no of $d's$
Push $a's$ into stack, pop them with $b's$ (as we need to check $m=n$ or not) , now if stack is empty and $c$ is in input, it means $m=n$ holds, now push $c's$ and then pop $c's$ with $d's$ , if stack again goes empty and we have nothing in input it mean $k=l$ (that is what we required) , accepted.
$L_2=\{a^mb^nc^kd^l\, |\, if(n=k)then(k=l)\}$
$L_2$ is not cfl.
Push $a's$ into stack, then Push $b's$ into stack , pop $b's$ with $c's$ (as we need to check $n=k$ or not), suppose $n=k$ holds, means when we get $d$ in input , we have $a's$ on stack. now we have to check $k=l$ , i.e, no of $d's$ = no of $c's$ , it is not possible as we don't have $c's$ now to check it.
