Well, I am trying to make a concept, mathematically, of this idea, and here is what I got.
Given an algorithm A there exists the Big-O(which is the representation of efficiency of a given algorithm, simply put http://en.wikipedia.org/wiki/Big_O_notation).
[math]A(x)\in O(g(x))[/math]
There are many possibilities that could occur within this concept, which is either that the other algorithms that branch off from algorithm A have Big-O's that add up to the Big-O of algorithm A or are the product of, or both?
Either that, whatever combination of functions of Big-O to get the function of the original Big-O.
[math]O(\delta) = \sum_{n=1}^{k}O(\delta _{n})=O(\delta _{1})+O(\delta _{2})+...O(\delta _{n})[/math]
[math]O(\delta) = \prod_{n=1}^{k}O(\delta _{n})=O(\delta _{1})\times O(\delta _{2})\times ...O(\delta _{n})[/math]
[math]O(\delta) = \sum_{n=1}^{k}O(\delta_{n} )\pm \prod_{n=1}^{k}O(\delta _{n})[/math]
Of course, this assumes that this conjecture is correct, which is that there is a conservation of information(?) when dealing with the break down of algorithms to their simpler form.