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Despite what official histories may say, it is quite clear that "the Universal Khan" had no serious plan to restore the Liao empire in East Asia after the Jurchen conquest. What if he did care about restoring the empire and invaded the fledgling Jurchen empire in 1135 (just after the death of Wanyan Wuqimai)?
Would the Khitans (Dashi's army + the Khitans still in the east) have success in regaining the empire? What about the Song, as the Jurchen armies are going to be drawn back north to face the Khitans? How would this change Islamic Central Asia, where the Qara Khitai have just left?