 Complete the following phrase:  The idea that the Roman Empire had grown too large to efficiently be managed by one emperor, and was more appropriately governed by two co-ruling emperors, had become established by the time of emperor Diocletian 284305 in the late 3rd century. Throughout the fourth century, various different divisions were made, until the empire was firmly and permanently divided into western and eastern spheres of imperial administration from the death of emperor Theodosius I 379395 in 395 onwards. Though modern historians typically use the terms Western Roman Empire and Eastern Roman Empire to describe the new political situation, the Romans themselves never considered the empire to have been formally divided, still viewing it as a single unit, although most often having two rulers rather than one. The Western Roman Empire, more rural than the east, with less people and a less stable economy, and prone to an increasing number of Germanic barbarian invasions and settlements, experienced catastrophic decline throughout the 5th century. In 410, the Visigoths under Alaric I had 