Find a CFG for the language $\{ x\$y \mid x,y\in\{a,b\}^* \wedge |x| \ne |y| \}$?
Hint:
$$
L = \{ \Sigma^{m+1} \Sigma^n \$ \Sigma^n : n,m \geq 0 \} \cup \{ \Sigma^n \$ \Sigma^n \Sigma^{m+1} \},
$$
where $\Sigma = \{a,b\}$.