This trivial DFIA has inputs $\Sigma = \{ a, b \}$ and outputs $\Gamma = \{x, y \}$. There are three states: an initial idle state $s_1$, a state $s_0$ in which output $x$ is performed, and a state $s_2$ in which output $y$ is performed. From each state, input $a$ brings the DFIA to state $s_0$ and input $b$ brings it to state $s_2$.