  We analyze quantitatively the interplay between explicit and implicit
renormalization in Nuclear Physics. By explicit renormalization we mean to
integrate out higher energy modes below a given cutoff scale using the
similarity renormalization group (SRG) with a block-diagonal evolution
generator, which separates the total Hilbert-space into a model space and its
complementary. In the implicit renormalization we impose given conditions at
low energies for a cutoff theory. In both cases we compare the outcoming
effective interactions as functions of the cutoff scale. We carry out a
comprehensive analysis of a toy-model which captures the main features of the
nucleon-nucleon (NN) S-wave interaction at low energies. We find a wide energy
region where both approaches overlap. This amounts to a great simplification in
the determination of the effective interaction. Actually, the outcoming scales
are within the expected ones relevant for the physics of light nuclei.
