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

$$L = \{x^r \# wxz | x, w, z\in \{a, b, c\}^*\}$$

That should make it clear that the language is context-free.