So... is D_Cide Traumerei the Animation finished or not?
YES, it is finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Ryuuhei Oda, haunted by his brother's mysterious death and a strange mark he saw at the scene, lives a normal life as a kickboxing high school student.
His life is turned upside down when he's bitten by a bizarre creature and starts having unsettling dreams.
He's then recruited by Jessica and Aruto, who reveal a hidden world of dream monsters and that he is a "knocker-up" capable of fighting them.
Ryuuhei must learn to control his newfound abilities and use his kickboxing skills to protect the city from these nightmarish threats, all while confronting the secrets of his past connected to that unforgettable mark.