An algebra for proper generating trees

We find an algebraic structure for a subclass of generating trees by introducing the concept of marked generating trees. In these kind of trees, labels can be marked or non marked and the count relative to a certain label at a certain level is given by the difference between the number of non marked and marked labels. The algebraic structure corresponds to a non commutative group with respect to a product operation between two generating trees. Hence we define the identity generating tree and the inverse of a given generating tree.