# Find a CFG for the language $\{ x\$y \mid x,y\in\{a,b\}^* \wedge |x| \ne |y| \}$? Consider the language below, on the alphabet$\Sigma = \{a,b,\$\}$: $$L = \left\{ xy \mid x,y\in\{a,b\}^* \land \left|x\right| \ne \left|y\right| \right\}$$

I need to define a CFG for this language. I've tried couple of CFGs but they all failed in one way or another.