> The mathematically rigorous form of the posed question is whether there is an algorithm with run time f(N) for which there exists strictly decreasing g(N) such that f(N) = O(g(N)). That is, the run time is bounded by a forever decreasing function.

Let's say my minimum runtime is 7, and the strictly decreasing bound on my runtime is g(N) = 1e15/N + 7

Doesn't that fit your description fine?