If there are new extremists born every day, who's fault is it ?
If the US persists the way it has done so far, it won't win.
Terrorists don't wage war, they wait (sometimes for decades) and act when we least expect it.
The ways fo the US to win are:
Don't interfere against them and in favor of their enemies.
If you think you should, then do it in such a way both sides
feel their demands are respected.
Let the nations where they come from solve their problem.
Be more careful with any kind of potential way for terrorists to do harm (infiltrate their organizations, secure planes, trains, put cameras everywhere, etc....).