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“remaining open question is related to the termination of flips and ascending chain condition (or finiteness) of local log canonical thresholds. We call this approach the original method. We are not aware of detailed references discussing the original method for higher dimensional klt pairs, and therefore we discuss this in detail in Section 3. Using the finiteness of weak log canonical models established in [BCHM], Hacon [Hac12] gives another approach to the Sarkisov program, which is called the double scaling method and is known to terminate in all dimensions. Both” (Wang 和 Chen, p. 2)