As long as Open Question 1 is answered in the positive – i.e. \(\textbf{P} \subsetneq \textbf{NP}\) – \(\textbf{NP}\)-complete problems thus fit the description of effectively decidable problems which are intrinsically difficult in the sense described in Section 1 .  As we are now about to see, however, they are by no means the hardest problems studied by complexity theorists. Nor is complexity theory incapable of making further distinctions about the difficulty of problems which lie inside \(\textbf{P}\) or between \(\textbf{P}\) and \(\textbf{NP}\) (presuming the latter class is non-empty).