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

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