When the US occupied TN and AR, and Texas was cut off from the rest of the Confederacy, the 5 Atlantic states of the Confederacy + Alabama were on their own. They were going to run out of forage, mules and horses, and become immobile, long before the ran out of men. The horses and mules eat more and they weaken and die first. The locomotives wear out, and without mechanics to repair them, become unusable. Attrition involves much more than battlefield deaths.Grant threw a series of left flanking movements which kept Lee's forces engaged. It was simply a tactic of attrition. The North had men and supplies. The South didn't.