One thing no one ever talks about that completely ruins the idea of zombies is that they still need energy. At a certain point, they would literally run out of the ions and nutrients needed to move their arms and legs which would render them useless.
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Even if they didn’t decompose. Your body destroys itself every time you move. Your cells are constantly reproducing to keep you from falling apart. If the cells weren’t working it wouldn’t be long until you were incapable of moving at all. I give zombies 4 weeks tops.