In our theoretical computer science class, we are currently working with undecidable problems on Compositional Message Sequence Graphs (CMSGs). We proved in the lecture, that the existence of a safe path of these graphs is undecidable.
We should now prove or disprove whether the following decision problem is decidable: Given GMSC $G$ and $k \in \mathbb{N}$. Question: Does G have some safe and accepting path of length at least k?
For instances of the problem with $k = 0$, the problem is identical to the problem proven in the lecture as the value of k does not restrict the path lengths. Therefore, the problem cannot be decided for any GMSC $G$ with $k = 0$.
Is this enough to prove that the homework problem is undecidable in general?