Deca-Dence

Many years have passed since humanity was driven to the brink of extinction by the sudden emergence of the unknown life forms Gadoll. Those humans that survived now dwell in a 3000 meter-high mobile fortress Deca-dence built to protect themselves from the Gadoll threat.

Denizens of Deca-dence fall into two categories: Gears, warriors who fight the Gadoll daily, and Tankers, those without the skills to fight. One day, Natsume, a Tanker girl who dreams of becoming a Gear meets surly Kaburagi, an armor repairman of Deca-dence.

This chance meeting between the seemingly two opposites, the girl with a positive attitude who never gives up on her dreams and the realist who has given up on his, will eventually shake the future course of this world.
(Source: Funimation)