I have two languages $C_1$ and $C_2. \left(\Sigma=\{0,1\}\right)$:
$C_1=\left\{xyz\mid x,z \in \Sigma^*, y \in \Sigma^*1\Sigma^*, \text{ where } |x|=|z| \geq |y|\right\}$, and $C_2=\left\{xyz\mid x,z \in \Sigma^*, y \in \Sigma^*1\Sigma^*1\Sigma^*, \text{ where } |x|=|z| \geq |y|\right\}$
I want to show that $C_1$ is a CFL, while $C_2$ is not a CFL. I'm trying to create a grammar / pushdown automata that accepts $L(C_1)$, but the $|x|=|z| \geq |y|$ part is throwing me off. I plan on using the pumping lemma for $C_2$, but I'm not sure which string to pump.