Given any total recursive function r(n), there exists a recursive language L such that for any Turing machine M recognizing L, say within time bound S(n), there exists another Turing machine M′ that also recognizes L but within a time bound S′(n) that satisfies r(S′(n)) ← S(n)
for all but a finite number of values of n. Thus for this language there can be no fastest program.
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