  We showed that the strong Sarkisov Program of dimension $d$ can be derived
from termination of certain log flips in dimension $\leq d-1$. As a corollary,
we show that the strong Sarkisov Program holds in dimension 4. Using the theory
of syzygies of Mori fibre spaces, we obtain a directed diagram that encodes all
the information of the strong Sarkisov Program.
