Why does the US allow Al-Qaeda to exist?

It seems there are alot of sleeper cells in the US. Thanks to US immigration. The Israelis keep a tight leash on muslims, so what if it's profiling if it keeps another 9/11 from happening. It seems the US wants to fight wars with liberal methods and not ruthless, merciless results. Know why Al-Qaeda is winning despite their numbers and major losses? Because they're prolonging the war, just like the Vietnamese did. Wearing us down. Al-Qaeda should be annihilated. No arrests, no trials, just execution. Kill'em all. These are terrorists here. Does anybody know what a terrorist is? Anyone. Anyone. Oh anyone at all?