We introduce the notion of a completely solvable complex real-holomorphic system of biholomorphisms and prove that such a system forms a discrete dynamical system. Then we define functional invariants and find the dimension of the basis of nondegenerate absolute invariants for the class of systems in question in general position. Finally, we obtain criteria of boundedness of the number of compact invariant hypersurfaces for auxiliary real systems of diffeomorphisms and then for complex real-holomorphic discrete dynamical systems.