On composite and non-monotonic growth functions of Mealy automata

We introduce the notion of composite growth function and provide examples that illustrate the primary properties of these growth functions. There are provided examples of Mealy automata that have composite non-monotonic growth functions of the polynomial growth order. There are described examples of Mealy automata that have composite monotonic growth functions of intermediate and exponential growth. The questions concerning the interrelation between the notions ``composite'' and ``non-monotonic'' of a Mealy automaton growth function are formulated.