Time Traveler (時間遡行, Jikan Sokō) is the second episode of the anime Munou na Nana. It adapts the second chapter (Volume 1, Chapter 2) of the manga.
Someone with the Talent to travel into the past and rewrite history compromises Nana's goals. Therefore, Nana sets out to befriend this individual and dispose of him to flatten any wrinkles in her plans.
Just getting out of the shower, Nana reads a message on her phone about Talented being a threat to humanity. A story is told involving a person who awakened to his Talent and destroyed a city thereafter, which after this, children with Talents are born. To facilitate the growing tension surrounding tension with the Talented, such people are implemented into the military, establishing a new police force. However, this caused an even bigger rift between the Talented and Talentless as the Talented used their abilities mostly for destruction, personal gain, etc. This caused a war to break out and in the end, the Talentless won the war. Decades past by and in that time, the nation's and people's thoughts and opinions on the Talented softened. In the present, Nations openly accept Talented users and train them in a consolidated and isolated manner in what's called "Training Academies". At this academy the students are trained to combat against the enemies of "Humanity" unbeknownst to them that they are the enemy. Nana was tasked by a superior to covertly kill all of the Talented at the school she's assigned.
In the present at the school yard, Nana is approached by Moguo and is asked if she's seen Nanao. Nana's left eye twitches once as Moguo details how posturing Nanao was to become the class rep, disappears without a trace. Moguo though confesses that Nanao was a bad ass when he displayed his power. Just then, another student named Michiru struggles with the training exercise by running across a log bridge above a placid lake. Also, another student by the name of Youhei is in a pinch, but Seiya helps him out by freezing the lake that he dangled above from. In Nana's deduction, Seiya who froze a lake 5 meters deep in mere seconds with his Talent, reinforces that Talented are a threat to humanity. This is all based on the sentiments that immature people will exploit their powers for their own personal endeavors. Affirmed to carry out her mission to dispose of all Talented, Nana is then tasked with stopping Moguo and Seiya's fight with the other.
Afterward, during lunch, Nana talks with Seiya about his freezing Talent. During this, Nana scrutinizes all of Seiya's responses to her questions noting every lie and omission he makes through his actions. The conversation then shifts to Nanao's absence, whereas the class still believes he's out sick. To that point, Nana resolves herself to deal with that situation before it escalates any further. An altercation between Moguo and his associate Shoichi, which is stopped by Youhei and his Talent. Youhei's Talent for stopping time is then revealed, but Nana has suspicions about that through her careful observational skills. From Nana's phone, Youhei's potential kill count is revealed to be over 800k+ people.
Later that day, at the cafeteria, Nana eats her meal with Youhei who despises Nana's loud eating, but Nana argues that he eats as loudly as she does. While stating she merely wants to talk with Youhei as she's a fan of his. Nana then tries to take a pickle of his while intentionally knocking over his glass of water, triggering his Talent. Youhei details that his Talent is to stop time, but Nana calls him out on his lie and blackmails him to tell the truth. To that, Youhei confesses his real Talent is reverse time travel. A Talent that allows him to change the course of the present by changing events in the past. Impressed that Nana deduced his Talent by what he believed to be by using her Mind Reading Talent, in truth, it was by her observations surrounding him. Feeling a kindred spirit bond with Nana, Youhei proposes that the two team-up to rebuild the unfair world together and extinguish the evils of the corrupt world they live in. Playing along, Nana agrees to Youhei's proposal noting that he's super-deluded. Right as the two go to shake hands in conformation to their partnership, Youhei notices that Nana she left grains of rice in her bowl and details he detests wasted food be left behind. Although on the outside, Nana is all smiles and will duly note Youhei's peeve, she innerly notes of how dangerous his Talent is and how it could compromise her goal immensely.
Out of nowhere, Kyouya appears and asks if Youhei can use his Talent to investigate Nanao's disappearance. Kyouya also states that he won't gossip to others about Youhei's Talent. Recalling that Nanao could be taking a sick day, Kyouya discloses the contrary evidence that disproves that notion. Furthermore, he inquires Nana what he was doing with Nanao as the two really hit it off and what she was doing with Nanao the day before. Calmly, Nana states that she merely congratulated him as the new class rep. Continuing with his interrogation, Kyouya carefully grasps Nana's hair, making her believe he's trying to cause her to slip up or use his Talent dig up the truth. Curious to know why Kyouya was grasping her hair, Kyouya answers he simply has to and detailing his sister also has pig tails. Wanting to gain control of the conversation, Nana changes the subject about Nanao being a possible enemy of humanity. It's then Nana claims that she heard a strange voice, detailing her Talent to being able to hear people's inner voices. Nana also states how Kyouya was abscent that day and how his apprehensive attitude toward Nanao contradicts his interest with Nanao's disappearance. When pressed for a reason, Kyouya merely smiles and leaves while stating he merely wished to make some friends. Youhei now suspicious of Kyouya, Nana notes that she's temporarily got Kyouya off her tail for now. With that settled, Youhei agrees to help, which pleases Nana on the outside, but on the inside, she's disgusted.
At the dorms, Youhei uses his Talent to investigate the past, and upon returning while heavily exhausted. He confirms that Nanao really didn't return to the dorms that night. Perceiving that Youhei's Talent is exhausting, to which, he confirms, Nana also notes that their must be other flaws to it as well. Learning more about Youhei's Talent by questioning him, Youhei goes back in time briefly, claiming the time before, someone spotted him before he could do a thorough search. Returning to the present, Youhei details to Nana that she and Nanao went to the cliff the day before. By the cliff side, Youhei now out of breath, is told by Nana that the two merely talked and parted ways after it. It's revealed that in the past, Nana noticed him and when their eyes locked, he was sent back to the present, which is one of the flaws to his Talent. Although Nana wants to try again tomorrow, Youhei is adamant to continue as 24 hours is his time limit. Also, proclaiming he wants to follow through his sense of justice, Youhei grows suspicious of Nana, claiming there maybe something in the past she doesn't want him to find out. Nana then details what time she last talked with Nanao before they "parted ways". Youhei then goes back in time, but not before claiming he's not doing it out of suspicion of him. Once Youhei is gone, Nana internally hopes that her past self can deal with Youhei before he's able to find her out and try and stop her. Upon his return, Youhei again was noticed by Nana, right before he could deduce how Nanao disappeared. Nana internally confirms what Youhei stated to him was true, noting her memories being overwritten from that experience. Confirming that Nana is no way the enemy of humanity, which pleases Nana.
That night at the dorms, Nana leads Youhei into the nearby forest, and confesses to him that Nanao was killed and eaten by an Enemy of Humanity there. Following Nana's words, Youhei goes into the past where he's sequentially killed by drowning in the frozen pond that Seiya used his Talent on earlier that day. As it turns out they were both standing above said frozen pond because Nana shoveled dirt over the area covered it up and the darkness helped hide it too.