The more you think about time travel and paradoxes the worse it gets. I always liked Star Trek's Captain Janeway's lin:
"Every time I think about Temporal Mechanics I get a headache."
The Terminator film is a classic example. Answer to the problem of the machines in the future: DON'T SEND ANYBODY BACK IN TIME. It was sending somebody back that started the whole mad affair in the first place.
It does give you a headache …