Did the treaty of verdun ever fulfill its purpose? i tried looking it up, but nothing came up. explain

The Treaty of Verdun was made to stop conflicts between Louis the Pious' sons over who would rule the Carolingian Empire. The treaty split the empire between the three and stopped the war, but did not resolve conflicts, seeing as one of those sons' son, Lothar II, then tried to conquer more of the empire for himself.