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    $\begingroup$ The class P is not about algorithms but about problems decoded in languages. The correctly phrased statement would be: "I tell you that this algorithm for problem X runs in time $O(2^n)$ but yet $X$ is in P." It might therefore even be true if the algorithm runs in time $\Theta(2^n)$, the problem could be in P, if we pick an inefficient algorithm. $\endgroup$ Commented May 4, 2015 at 7:59