# Is this language L context-free?

The language

$$L = \{x^r \# y | x, y \in \{a, b, c\}^*\\ \text{ and }x\text{ is a contiguous sub-string of }y\}$$

where $$x ^ r$$ denotes the backward written word x, is context-free.

Can someone explain, if this statement is true? I am not able to construct a PDA, so I think the language is not context-free. Does anyone have an idea how to prove it?

A more precise expression of the condition "$$x$$ is a contiguous substring of $$y$$" produces
$$L = \{x^r \# wxz | x, w, z\in \{a, b, c\}^*\}$$
• @x_x: since they are both unconstrained, they are just $\Sigma^*$, which should not be hard to write a grammar for. – rici Feb 28 '19 at 0:22