  It has been conjectured by Prokhorov and Shokurov that the moduli part in the
canonical bundle formula is effectively b-semiample. In this work we reduce
this conjecture to the case where the base of the fibration has dimension one.
Moreover, in the case where the moduli part M is numerically trivial, we prove
the existence of an integer m, that depends only on the middle Betti number of
a canonical covering of the fibre, such that mM is linearly equivalent to the
trivial bundle.
