One would think that the first thing to establish when you have a reliable time machine is whether or not time is mutable. If your theory of time travel is complete you would know it before you built it. You certainly would not fight the war while that is still an open question.That depends on whether the characters knew it was immutable. For example... in the first Terminator movie (taken by itself, and ignoring the sequels), Skynet clearly believes that the past can be altered. But the timeline we're eventually presented with is circular -- Kyle Reese always went back, since John Connor wouldn't exist otherwise, to send him back later. Sarah Connor was radicalized into the person who raised John to defeat the Terminators, because the Terminator came back. The events are self-consistent, and there is only one timeline. It was the very attempt to alter the past that created it.