But the Guide mentions that "late on the third day, the Aiel finally carried out their purpose of killing Laman of Cairhien, and during that night managed to concen­trate their forces on the east side of the Erinin."

I think it's also mentioned in the series, or at least naturally assumed, that the Aiel killed Laman (and his brothers) and took Laman's sword.

Still, would be cool, if Tam was actually responsible for ending the Aiel War. But not sure, if this isn't ruled out.