Patema Inverted: Beginning of the Day

Bored with her claustrophobic underground world, Princess Patema explores the danger zones where terrifying creatures called Batmen reportedly lurk. One day she discovers a huge shaft that disappears into the darkness above and below. After an encounter there with one of the Batmen, Patema finds herself in a topsy-turvy world unlike anything she has seen before and forced to come to grips with a solitary boy, Age, who has, from her point of view, a very surprising outlook upon things.

Synopsis from Anime News Network