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 𝑥,

if 𝑄(𝑥)=𝑌𝐸𝑆 then there is a string 𝑦 such that 𝑉(𝑥,𝑦)=𝑌𝐸𝑆, if 𝑄(𝑥)=𝑁𝑂 then for all strings 𝑦, 𝑉(𝑥,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?