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On the rooftop with over 200 combatants, all fighting their exact duplicates, one pair was battling much differently than the others. Compared to the other girls, who were dominating each other sexually in various ways, this pair was battling in the most efficient way possible. Every strike was planned, aimed towards the exact coordinates that'd damage the most important organs, just enough force to rupture such organs while using minimal energy, and with the perfect technique to cause maximum pain. This story doesn't feature any blood however (much to a certain girlfriend's dismay), as the two were able to perfectly predict each other's moves and block them accordingly. The name of both girls was Eiai Nano.

When Nano first gazed upon her doppelganger, she saw the many ways her efficiency could be increased with a doppelganger. She now had the ability to do two things at once, making it so that all schoolwork could be done in half the time. If one of them went to half of her classes and the other went to the other half, the workload Nano would then have to deal with would essentially be halved. In her pursuit to graduate to a good school and obtain a prosperous career, doing such a thing would only be of assistance.

But after the the Makes-You-Want-To-Fight-Your-Clone-In-Order-To-Prove-Who-The-Original-Is drug clouded her vision, she started to notice the inefficiencies of having a doppelganger. Eiai Nano being doubled would mean food consumption would be doubled. Eiai Nano being doubled would mean water usage would be doubled. Eiai Nano being doubled would mean oxygen consumption would be doubled. It was simply a fact of life that maintaining multiple human lives required more resources than maintaining a single human life, and that wasn't very efficient.

So what was the most efficient option in such a situation?
Extermination.

The two tried to end each other in the most efficient way possible, but in the nanoseconds it took to prepare their attacks they noticed the exact same tensing of the muscles and readying of the posture coming from each other. An analysis showed that the two were attempting the same moves at the same time, which meant they needed to prepare extra precautions to attempt to block such moves. Yet it would appear that they were doing the same thing yet again, so they would need to alter their attack to circumvent or hit through the block in the nanoseconds left preparing it...

That left them like this, dishing out and blocking identical attacks. The two had some sprains and red eyes and a few other minor injuries, but neither seemed to be overpowering the other. It looked like the fight could continue like this for some time, but they were interrupted before it could continue long.

"Stop this at once!"
"You're sullying your beauty!"

A beautiful girlfriend by the name of Mimimi, and her doppelganger, separated the fighting duo.

"You're one of the most beautiful ladies in the entire world," Mimimi said as she pried Nano away from Nano. "Behind me of course."

"Fighting in such a barbaric way would tarnish your beauty," Mimimi said as she pried Nano away from Nano. "It'd be a waste of such good looks!"

"This is the most efficient way to eliminate a doppelganger."
"I simply desire to get such a detested lifeform out of my sight."
The two Nanos answered simply, their voices calm as if they weren't full of rage within.

"You can't sacrifice your beauty for something like that!"
"Your beauty is important! Don't sacrifice your beauty!"
The Mimimis dragged the Nanos away from each other in near tears, and after some time eventually managed to convince them to stop their current battle. Such convincing would take up 99% of the story if listed out here, so most of it has been cut out for your convenience.

"I understand," Nano said. "I shall make an attempt to battle while preserving my own beauty."

"I do have to ask though," Nano said. "How does one battle while preserving their beauty?"

The Mimimis smiled warm yet smug smiles.
"Well obviously you just need to compare some of the beautiful parts of you with each other!"
"A battle where one compares the beautiful parts of themselves, start of with the titfight!"

"Titfight?"
"Such a word isn't in the dictionary."

"It's a simple yet beautiful way for two with such beautiful breasts to fight, naturally!"
"This form of battle where one compares the beauty of her breasts to another is perfectly suited for you naturally!"

The Nanos brought out measuring tapes and-

"Oh no no," Mimimi said. "Naturally you won't be comparing your breasts like that."

"It's a competition between breasts," Mimimi said. "Naturally the two of you have to try and flatten each other's chests."

The Nanos, now completely understanding, brought out baesball bats and-

"NOT LIKE THAT!"
"WHERE'D YOU EVEN GET THOSE!?"

It took some time, but the Mimimis eventually pried the bats out of the Nanos' hands.

"For now just use your hands," Mimimi said. "We'll just start with that, naturally."

"Beautifully caress each other's breasts," Mimimi said. "And you'll be able to settle this, naturally."

The Nanos just followed through, not really understanding it. They had already determined just by looking at each other that their breasts were the exact same shape and size and color and firmness, there was a 0.03% chance of any differences being found. For now at least they were willing to entertain the Mimimis' idea, squeezing and groping and rubbing the breasts in front of them over and over and over...

Steam erupted from the blushing red faces of the Nanos, their vision blurring and tingles springing throughout their bodies. They were malfunctioning, having each other touch their breasts was making them unable to focus. Sexual thoughts were filling their heads, very inefficient for the immediate circumstance. If they were to quantify their level of arousal right now, it'd be 10%. Even at this much it made them struggle to think.

Nano took a few breaths and tried to calm herself down. She needed to get herself back on focus. Reciting the digits of pi always calmed her down. And so she started to count.

"3.141592653589793238462643383279502884197..."
"3.141592653589793238462643383279502884197..."

The two of them started their count, doing the best they could to focus on the numbers and not on their breasts. Numbers are simple and logical. The digits of pi are the exact same at every moment and efficient at their job. If there is one thing that could ground her to reality, it should be pi.

"169399375105820974944592307816..."
"169399375105820974944592307816..."

The two continued, still unable to completely get their minds off of each other's touch. Their voices distracted each other, the numbers starting to drift from their minds as they focused more and more on each other's lips.

"40404040..."
"40404040..."

Their count was starting to get off track, the two starting to repeat the numbers they heard each other say. They couldn't think about anything other than their pleasure, leaving their mouths on autopilot as they continued to pleasure each other more and more. If they were to quantify their level of arousal right now, it'd be 32%. It was starting to grow rather quickly, and it was beginning to overwhelm them.

"This sort of competition is not leading to any succinct conclusions," Nano said.

"Utsukushisugi Mimimi, I desire to know the next steps of action," Nano said.

"Huh!? Oh-"
"Yes... naturally..."
The Mimimis, who were practically melting from the beauty before them earlier, snapped back to reality upon hearing the Nanos.

"Well um..." Mimimi stumbled over her words before calming herself down. "Maybe now you should take the chance to compare your breasts directly."

"Y-Yeah." Mimimi needed some time to get her head together. "Naturally you just need to put your breasts together and compare their strength."

"Understood."
"Understood."
The Nanos took off their shirts and-

"Y-YOU DON'T NEED TO DO THIS NATURALLY!"
"Y-YOU CAN KEEP YOUR CLOTHES ON NATURALLY!"

"But this would be far more efficient," Nano said.
"Clothes would only impede the current battle," Nano said.

The Mimimis tried to respond, but it was impossible as they saw the Nanos unclip their bras. Such beautiful and perfect skin with a shiny gloss and perfect areolas and nipples that just made them want to reach out and touch them with and...

The Mimimis collapsed onto the ground, feeling like they'd melt into a pile of slime.

The Nanos pushed their breasts towards each other at a speed of 7.2 millimeters per second, aligning their nipples at least 99.9% perfectly before smashing them into each other. In less than a nanosecond the two felt a sudden jolt of pleasure, pleasure that made anyone else want to shriek. If they were to quantify their level of arousal right now, it'd be 51%. It jumped incredibly quickly and it was continuing to rise, faster and faster and faster and faster.

Nano and Nano increased the level of force they used, progressively pushing their nipples harder and harder into each other. They couldn't even start listing the digits of pi with the amount of pleasure they felt, which was so much that steam seemed to burst from their ears. Their nipples were tingling, warm with pleasure that seem to burst through their entire bodies. If they were to quantify their level of arousal right now, it'd be increasing at an incredible rate.

The two put their hands on each other's shoulders, having become so weak they could nearly fall over. The speed at which their arousal was growing was seemingly exponential, their breaths were growing ragged and their faces were red hot. Their arms went down to each other's skirts, slowly creeping below and to each other's panties. It was clear that the only way to separate them was to make one of them climax, and this was the most efficient way to make one of them go down first.

Nano couldn't explain it, but she started to understand how this was meant to differentiate them. As the two of them pumped their fingers in and out of each other over and over again, the two found themselves determined to be the last one standing. When Nano gazed upon her doppelganger she saw a stale and unemotional copy, like some robot that claimed to be her. Maybe beating her doppelganger would show that she's the original, she's the one here meant to date Rentaro, she's the one that belongs with this family. If they were to quantify their level of arousal right now, it'd be 99%.

Their bodies were quaking, barely able to hold it all in. If they tried to recite the digits of pi now they'd only be able to say the number 3. Their legs felt like jelly, they should've collapsed long ago. They could barely keep their heads up, their faces falling slowly towards each other until their lips met.

The kiss was cold, robotic, yet at the same time it wasn't bad. It was a quick and efficient kiss, yet that was enough.

If they were to quantify their level of arousal right now, it'd be 100%.
The two absolutely burst, shaking as an orgasm seemed to absolutely wreck her. Nano wasn't one to masturbate, she figured it was only useful for inducing arousal and as such was inefficient, but she never expected the level of arousal to be this much. She couldn't control herself, her hands letting go of her doppelganger and her legs completely collapsing as the pleasure was too much for her to bear.

"Fweh..."
"Fweh..."
A small and cute noise that one wouldn't expect to come out of such logical beauties escaped the Nanos' lips, the two seemingly breaking down as they slumped unconscious on the floor. It appeared this line of combat wasn't efficient when it came to differentiating them, so a second trial was to ensue upon reawakening.

But until then they had an efficient nap, with efficient dreams, recharging their energy for an efficient battle.

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