But at the same time, a consensus has also developed that it is unlikely that we will be able to settle the status of \(\textbf{P} \neq \textbf{NP}?\) on the basis of currently known methods of proof. A familiar example is the method of diagonalization, as employed in the proof of the undecidability of the classical Halting Problem (from which it follows that the recursive languages are properly included in the recursively enumerable ones). We have seen that a variant of this method can be used to show \(\textbf{P} \subsetneq \textbf{EXP}\) in the proof of Theorem 3.1. But diagonalization proofs yielding such separations typically relativize to oracle-based computation in the following sense: if such a proof yields \(\textbf{C}_1 \neq \textbf{C}_2\) for complexity classes \(\textbf{C}_1\) and \(\textbf{C}_2\), then a suitable modification will also typically yield \(\textbf{C}^A_1 \neq \textbf{C}^A_2\) for all oracles \(A \subseteq \{0,1\}^*\).[41]  Baker, Gill, and Solovay (1975) famously established the existence of oracles \(A\) and \(B\) such that \(\textbf{P}^A = \textbf{NP}^A\) and \(\textbf{P}^B \neq \textbf{NP}^B\). As we would expect a proof of \(\textbf{P} \neq \textbf{NP}\) based on diagonalization to relativize to both \(A\) and \(B\), this suggests that it is not possible to use this method to separate \(\textbf{P}\) and \(\textbf{NP}\).