I am looking for a anime?

ok the is a fighting anime set in a post apocalyptic world where monsters and beast roam live on the land and the humans live on some sort of machine in a town that could move. the main character in the anime is a teenager i guess who was part of the powerful group that travels around a slays the monsters and beast. then something happens that makes the higher ups strip him of he's title and put him in one of the town where he is sent to go to a academy of fighters. one he's first day he save a woman from a falling pillar and then he is put in a group that is lead by a girl. the last thing i remember is that he has some what of a special sword.