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Paradox of grandfather in Vs Match

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So I've been thinking about a fight (which I won't say because I want it to be a surprise) the question is that one of the sides has how Win with time travel, no one has Acausality so time travel works


the question, if he travel to the past to kills his opponent, then there is no fight, so he doesn't travel to the past so he doesn't kill the opponent, the cycle re-start since he don't know that happen....

Could we consider this a win or not?
 
So I've been thinking about a fight (which I won't say because I want it to be a surprise) the question is that one of the sides has how Win with time travel, no one has Acausality so time travel works


the question, if he travel to the past to kills his opponent, then there is no fight, so he doesn't travel to the past so he doesn't kill the opponent, the cycle re-start since he don't know that happen....

Could we consider this a win or not?
But my dearest Multiverse theory...
 
Alright. I'll answer your question the right way now.
So I've been thinking about a fight (which I won't say because I want it to be a surprise) the question is that one of the sides has how Win with time travel, no one has Acausality so time travel works


the question, if he travel to the past to kills his opponent, then there is no fight, so he doesn't travel to the past so he doesn't kill the opponent, the cycle re-start since he don't know that happen....

Could we consider this a win or not?
Assuming that time will resume its course once changes are made, I conclude that the killer wins because they do not depend on A for their continued existence.

A faces B. B will time travel to kill A. Time paradox triggered. Neither combatant is Acausal. Starting from the past, any resulting changes apply to both. A disappears, B is sent back to where they would have been had A never existed. When present time comes, B won't time travel...but it's unnecessary because this timeline's whole premise has become one where A does not exist. B never dies after killing A. → At best for A, the timeline adjusts once and they die. At worst, this is a stable time loop where B continually kills them for the rest of eternity.
 
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