  In this paper, we construct explicitly a noncommutative symmetric (${\mathcal
N}$CS) system over the Grossman-Larson Hopf algebra of labeled rooted trees. By
the universal property of the ${\mathcal N}$CS system formed by the generating
functions of certain noncommutative symmetric functions, we obtain a
specialization of noncommutative symmetric functions by labeled rooted trees.
Taking the graded duals, we also get a graded Hopf algebra homomorphism from
the Connes-Kreimer Hopf algebra of labeled rooted forests to the Hopf algebra
of quasi-symmetric functions. A connection of the coefficients of the third
generating function of the constructed ${\mathcal N}$CS system with the order
polynomials of rooted trees is also given and proved.
