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Farts come from food being broken down. You would have to draw a line between what is food you ate and what is gut bacteria. If the gut bacteria were to run completely out of food to break down and began breaking down weaker species of gut bacteria, that would probably produce farts. Does this mean that the digested gut bacteria became food? Semantics. What about if you swallow air and fart it out, is it really a fart? Again semantics.
So to answer your question OP, farts come from your butt.
