Kei and Yuri were originally junior auxiliary agents in the Worlds Works and Welfare Agency (W.W.W.A. or 3WA for short) when the two were paired together under the codename Lovely Angels. Kei was coming off her fourth probation for something she had done, and Yuri's dating exploits were common knowledge, not to mention the two had an instant dislike for each other when they met. At first, Kei and Yuri refused to work with each other, and Kei even resigned from the 3WA. Afterwards, the two continued to work together, although they earned their nickname, the Dirty Pair because of all the collateral damage the two (unintentionally) cause in the completion of their cases. And even though the two now get along with one another, they continue to bicker and complain to each other. Although it is often said that these are younger versions of the original Lovely Angels Kei and Yuri, in truth this series is an alternate universe telling of Dirty Pair, set in the years 2248-49. (Source: Wikipedia)

Third season of Yatogame-chan Kansatsu Nikki.

The virtual world inside the scub coral (intelligent coral-like lifeforms) created by Eureka... The people from that virtual world appeared on Earth ten years ago when it collapsed. Since this large-scale amalgamation, the humans from the virtual world call themselves Green Earth and the original Earth humans call themselves Blue Earth, and they've come to cause various conflicts with each other repeatedly below the surface. Eventually, Dewey Novak, a senior officer in the Green Earth Armed Forces, rises together with his comrades and finally sets a large-scale terrorism plan into action in order to protect their own dignity. Meanwhile, Eureka, who is detested by the world as the main cause of the chaos, has become a high-grade combatant with the UN's A.C.I.D. unit. Live in order to keep this world at peace... This was the path of atonement she chose. One day, she receives an order to protect a girl named Iris, a new Eureka who has the ability to control scab coral. They fight a lot at first but gradually come to understand each other through their lonely escape. Soon the world faces a crisis, and when that happens, Eureka draws on every last ounce of her strength as she fights. I want to protect Iris and this world. What future awaits her at the end of that wish of hers? (Source: Crunchyroll)

OVA bundled with 4th volume of manga.