How do you determine if a language falls into NP?

Question

for example, I know that the language

isnt context free by the pumping lemma for CFLs, but how would i prove that it falls into NP and not exp. time, decidable languages, or turing recognizable?

EDIT: Did some digging, and one oversight i made is that problems in NP are those that a verifiable in polynomial time BY a Nondeterministic Turing Machine. How would I know: a: There is a verifier that exists for this language in polynomial time and b: a NDTM can recognize it