Complex sentence: The Conradines, counts in the Franconian Lahngau region, had been loyal supporters of the Carolingians; they competed vigorously for predominance in Franconia with the sons of the Babenberg duke Henry of Franconia at Bamberg Castle.
Split into simpler sentences: The Conradines, counts in the Franconian Lahngau region, had been loyal supporters of the Carolingians. At the same time, they competed vigorously for predominance in Franconia with the sons of the Babenbergian duke Henry of Franconia at Bamberg Castle.