If initial attempts to find an efficient algorithm for solving a problem \(X\) which is known to be decidable are unsuccessful, a common strategy is to attempt to show that \(X\) is \(\textbf{NP}\)-complete. For assuming \(\textbf{P} \subsetneq \textbf{NP}\), it then follows from the Cobham-Edmonds thesis that no feasible algorithm for solving \(X\) can exist.