Infinitely generated semigroups and polynomial complexity

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.