Did ancient or medieval warriors "substitute" in and out of combat?

My answer will demonstrate that human beings wear out very quickly in combat. When I say "combat" I don't mean standing behind cover and watching your enemy on the other side of the street, or being in the same grid square as enemy combatants, or marching across a field to engage the enemy while your cavalry units soften up the enemy lines. When I say "combat", I mean swinging your sword at your enemy, fighting to end the other guy's life in order to save your own, or grappling in the dirt with knives.

I assert that human beings cannot physically sustain hard combat for more than a short number of minutes. Anybody that thinks they can, I think has never had to fight, or trained for any physical activity as exhausting as combat sports. My answer will demonstrate that regardless of whether or not we have evidence of combat relief in historical battles (despite the fact that it does exist), that the lack of capacity for sustained combat in human beings would require that relief was provided in these battles. We may not know exactly how they relieved one another on the front lines, or how often, but I'll show you that it would have had to happen, and it would have had to happen fairly regularly, because even exceptional and legendary fighters wear out quickly in combat, on the order of minutes.

For my first trick, I'll use a comment under the answer to provide some actual evidence of what I'm saying: Combat sports and martial arts. Mixed martial arts (MMA) fighters are hand-to-hand combatants with no weapons and no armour fighting in ideal conditions: They're well-rested beforehand (e.g. no forced march, well-fed, ample time to sleep the night before), they're fit for the fight, and they've been training for sometimes years beforehand. This video demonstrates a trained fighter in a state of exhaustion at the start of the third round. MMA fights are individual rounds of five minutes (which is on the far end of round length in combat sports) with an entire minute between rounds to sit and rest. If humans can sustain long bouts of combat, why isn't this done in all of the various kinds of combat sports? The answer is because humans cannot sustain long bouts of combat, and rounds are broken by rest specifically because of this fact. I think it stretches credibility to try and say that human beings can sustain long stretches of combat, provided that every sport -- and especially combat sports -- provides short rounds broken by periods of rest for the competitors.

For example, here are the rules for UFC, a specific brand of mixed martial arts, which stipulates that even a championship match "is to be for 5 rounds, each round no more than 5 minutes duration, with a rest period of 1 minute between each round." Then take a look at this discussion about boxing on Wikipedia. In particular, they talk about the length of championship boxing match being between ten and fifteen rounds of a couple minutes each, with a full minute of rest between each of the rounds. Here are some rules for swordfighting matches, which specifies that the "round lasts for 60 seconds, 60 seconds rest between each round." And here is the Wikipedia page for Combatives training, the hand-to-hand combat taught the US Army infantry soldiers, which provides a competition where the "fight consists of one ten-minute round."

Modern soldiers in combat use a couple of techniques to relieve one another from sustained combat, even while advancing on the enemy. One of those maneuvers is a flanking maneuver, which provides some relief to the soldiers on the immediate front while also pressing the advantage against the enemy: "Even when not entirely successful, for example at Anzio these operations can relieve pressure on troops on the main battle front, by forcing the enemy to divert resources to contain the new front." There is also what we in the infantry call "bounding" or "bounding overwatch", which allows a second soldier or group of soldiers to advance on an enemy position and take up a new fighting position, and thereby relieve the first soldier or group of soldiers and enable them to maneuver. These most basic infantry tactics have relief built directly into them.

And for my own touch of anecdote, since that seems to be totally acceptable, I was in the US Army infantry for twelve years and deployed four times, and I've spent most of my life training and competing in martial arts of various kinds. I have to say, if you think you're going to outlast any of these trained athletes or soldiers and sustain a hard fight for more than a handful of minutes at a time, you're in for a surprise. Regardless, I encourage you to get out there and take up martial arts (or join the army) and see for yourself! Fighting is hard.

From Book 3 of Caesar's Gallic Wars, Chapters 4 through 6:

Chapter 4

.... Our men at first, while their strength was fresh, resisted bravely, nor did they cast any weapon ineffectually from their higher station. As soon as any part of the camp, being destitute of defenders, seemed to be hard pressed, thither they ran, and brought assistance. But they were over-matched in this, that the enemy when wearied by the long continuance of the battle, went out of the action, and others with fresh strength came in their place; none of which things could be done by our men, owing to the smallness of their number; ...

Chapter 5

When they had now been fighting for more than six hours, without cessation, and not only strength, but even weapons were failing our men, and the enemy were pressing on more rigorously, and had begun to demolish the rampart and to fill up the trench, while our men were becoming exhausted, and the matter was now brought to the last extremity, P. Sextius Baculus, a centurion of the first rank, whom we have related to have been disabled by severe wounds in the engagement with the Nervii, and also C. Volusenus, a tribune of the soldiers, a man of great skill and valor, hasten to Galba, and assure him that the only hope of safety lay in making a sally, and trying the last resource. Whereupon assembling the centurions, he quickly gives orders to the soldiers to discontinue the fight a short time, and only collect the weapons flung [at them], and recruit themselves after their fatigue, and afterward, upon the signal being given, sally forth from the camp, and place in their valor all their hope of safety.

Chapter 6

They do what they were ordered; and, making a sudden sally from all the gates [of the camp], leave the enemy the means neither of knowing what was taking place, nor of collecting themselves. Fortune thus taking a turn, [our men] surround on every side, and slay those who had entertained the hope of gaining the camp and having killed more than the third part of an army of more than 30,000 men (which number of the barbarians it appeared certain had come up to our camp), put to flight the rest when panic-stricken, and do not suffer them to halt even upon the higher grounds.

Certainly there were no wrist watches, or even chronometers, on any of the battle participants, so time spans must be taken with a grain of salt, but it certainly must be clear that both sides thought it completely normal for weary combatants to step out of the line occasionally to rest. And further that the lengths of time that soldiers of the period could sustain active combat was substantially greater than the 2 to 5 minutes proposed elsewhere.

More notable than the timespan quoted is that the Gauls had time to "begin to demolish the rampart and to fill up the trench" while the battle progressed to its climax. That certainly was more than the work of just a few minutes.

Also note that the practice is so ubiquitous that it is only mentioned in consequence of the inability of the Romans to spell each other, due to being so badly outnumbered.

My answer here describes two additional occasions when Caesar describes the Gauls as practicing a continual relief of tired first-line troops.