Algorithmics course, please explain thoroughly, I'm trying to understand.

5. (hard, 20pt) Notice that a PDA could have a move that does not read from the input (only performs stack operation and state transition). Therefore, it is possible for the PDA to run forever on some given input. Prove that there is an algorithm that answers whether, for a given PDA, there is an input word on which the PDA has an infinite execution