On complexity of formal coding method for analysis of generator with monocycle substitutional transition function

Here we investigate autonomous automata with automaton states being binary $n$-dimensional vectors and transition function being a monocycle substitution. The complexity $T_n$ of solving gamma generating equations system by formal coding method is estimated asuming the number of equations is not constrained. Bounds of $T_n$ are obtained by estimating line complexity and the order monomial sets for the output functions sequence. It is stated that $TL(2^{n-1})<T_n<TL(2^n)$ where $TL(m)$ is a complexity of solving linear equations system of size $m\times m$ over field $\mathrm{GF}(2)$.