We present the dynamical system of an $A+B\rightarrow C$ bus loop system, served by two buses $X$ and $Y$. Here, there are three bus stops $A, B$ and $C$ in a loop where $X$ picks up people from $A$ and $B$ whilst $Y$ picks up people from $B$ only. Everybody alights at $C$, and no one boards from $C$. Thus, this is referred to as a \emph{semi-express} bus system where $X$ is a normal bus whilst $Y$ is an express bus that serves $B$ directly to $C$. We enumerate the exact state transition rules for this system, and find that it behaves in a complex manner where $X$ and $Y$ generally move around the loop aperiodically. Furthermore, we derive an approximate analytical 10-d map to calculate its Liapunov exponents and find that the largest one is positive, implying sensitivity to initial conditions. Hence, this semi-express bus system is a chaotic system. Intriguingly, this semi-express configuration is more efficient than fully express buses or normal buses where the commuters' average waiting time for a bus to arrive is actually lower.
