So... is Mushibugyou finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished before the manga:
Anime finished: September 30, 2013
Manga finished: September 20, 2017
We could not confirm the source content in MangaUpdates.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Edo is under attack by giant, monstrous insects that regular people can't handle. To combat this threat, a special group of warriors known as the Insect Magistrates are assembled, each possessing unique skills and fighting styles.
A powerful swordsman, Genjuurou Tsukishima, is called upon to reinforce their ranks, but due to circumstances, his son, Jinbee, goes in his place.
Jinbee, seeking to prove himself and overcome his past failings, journeys to Edo to join the Insect Magistrates. He is determined to become a stronger samurai and protect the city from the terrifying insect menace, facing numerous challenges along the way.