ITT: We talk about time travel

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I've been thinking a lot about time travel and how different "rules" would affect different actions. Pic related is a diagram I made for if a time traveller went back in time to kill himself. Point A is just before his birth, and Point B is when he time travels. The traveller follows the red line and performs the act. He then enters the blue timeline in which his birth was prevented but he still exists. However, the original timeline is still intact, and proceeds along the green line as if the traveller disappeared at point B.

Thoughts?