Given an algorithm, decide whether it runs in polynomial time?

This problem is not decidable (reducible to halting problem) but is semi-decidable and therefor verifiable (as those two definitions are equivalent: How to prove semi-decidable = verifiable?).

However, is this problem poly-time verifiable? A decision problem 𝑄 is in poly time verifiable iff

there is an algorithm 𝑉 called verifier such that V runs in $ O(x^{c})$ for some constant c for all inputs π‘₯,

if 𝑄(π‘₯)=π‘ŒπΈπ‘† then there is a string 𝑦 such that 𝑉(π‘₯,𝑦)=π‘ŒπΈπ‘†, if 𝑄(π‘₯)=𝑁𝑂 then for all strings 𝑦, 𝑉(π‘₯,𝑦)=𝑁𝑂.

Example: for an enumeration of P (such as this): How does an enumerator for machines for languages work? for each string $ p$ in the enumeration, does there exist some other string (certificate) $ c$ that allows you to verify $ p$ is a member of the enumeration in poly time?