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but since this model of simulation is rather involved, it is not included here.
Observe however that an identical argument as above then implies that <math>DTIME(r(f(2m+1)))</math> is not contained within <math>DTIME(f(m))</math> if <math>r(f(|M|+|x|))</math> is a function which gives a time within which it is possible to simulate a machine <math>M</math> with time complexity <math>f(n)</math> on input <math>x</math>.
==Non-deterministic time hierarchy theorem==
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