  We prove that any sequence of 4-dimensional log flips that begins with a klt
pair (X,D) such that -(K+D) is numerically equivalent to an effective divisor,
terminates. This implies termination of flips that begin with a log Fano pair
and termination of flips in a relative birational setting. We also prove
termination of directed flips with big K+D. As a consequence, we prove
existence of minimal models of 4-dimensional dlt pairs of general type,
existence of 5-dimensional log flips, and rationality of Kodaira energy in
dimension 4.
