When he interrogated Vyncent last time, Arthur knew that the disciples from his sect were supposed to get people from all the three powers and the female he killed on the Spirit Boat was probably the one who was sent to the Naga Tribe. This made his trip to their territory pointless and a complete waste of time.
With this in mind, he was more or less sure that the prince and his sister are most likely not in this world, or at least, not in this barren land. He had nothing to do here so it was time for him to cross the wall of Yang Fire, however, before that, he had to pay a visit to a certain someone.
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Dark Desert City is a large city situated at the center of the three factions, no one was controlling it but all three powers had some experts stationed here to observe the movements of their enemies. Some small-scale fights would occur but nothing too major, especially inside the city as it is forbidden fight or else the city lord guards will execute them on the spot.