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The provably asymptotically fastest algorithm within a factor of 5 for formally described problems will be constructed. The main idea is to enumerate all programs provably equivalent to the original problem by enumerating all proofs. The algorithm could be interpreted as a generalization and improvement of Levin search, which is, within a multiplicative constant, the fastest algorithm for inverting functions. Blum's speed-up theorem is avoided by taking into account only programs for which aarXiv:cs/0102018v1 fatcat:mvn3z5p5tnabvhu5id6qyvv6he