Things become different at infinity. A school example - if you count the number of even numbers up to 100, there are half as many of them as all numbers. And at infinity, every natural number corresponds to an even number. And it turns out that there is an equal quantity of each of them. Without limiting the quantity of numbers, it is impossible to mathematically prove that there ar fewer even numbers than all numbers. A similar story is observed in complexity theory. In this paper, using a lazy Turing machine, it is proved that for programs with infinite length, the maximum complexity is O(n). And one of the consequences of this fact is that P = NP at infinity. And because of this, as one of the consequences of the last statement, it is impossible to prove that P ≠ NP without limiting the program’s length. In time hierarchy theorem, diagonalization implicitly limits the program’s length. We need a similar trick to keep progress going.