  This paper continues the functional approach to the P-versus-NP problem,
begun in [1]. Here we focus on the monoid RM_2^P of right-ideal morphisms of
the free monoid, that have polynomial input balance and polynomial
time-complexity. We construct a machine model for the functions in RM_2^P, and
evaluation functions. We prove that RM_2^P is not finitely generated, and use
this to show separation results for time-complexity.
