# Time complexity analysis of 2 arbitrary algorithms – prove or disprove

We are given 2 algorithms A and B such that for each input size, algorithm A performs half the number of steps algorithm B performs on the same input size.

We denote the worst time complexity of each one by $$g_A(n),g_B(n)$$

Also, we know there’s a positive function $$f(n)$$ such that $$g_A(n)\in\Omega(f(n))$$

Is it possible that $$g_B(n)\in\Omega(f(n))$$? Is it necessary?

It seems naive to think that it’s necessary, but I can’t figure out to contradict it.