Language is $B = \{w \in \Sigma^* \mid w = a^n\#b^{2n}\#a^n \text{ for some } n \in \mathbb{N}\}$.
Assume the alphabet is $\Sigma = \{a, b, \#\}$.
I know this language is not context-free.
But below is a PDA that accepts all words from the above language:
But isn't this a contradiction? How can the language not be context free and still be recognized by a PDA?