Example of reactions series A → B followed by A + B → 2 C

I'm currently writing about geometric numerical integration and I need an example of the following series of chemical reactions:


\begin{align}
\ce{A &->[$k\_1$] B} \tag{R1} \\
\ce{A + B &->[$k\_2$] 2 C} \tag{R2}
\end{align}


The reason I want to use this form of the reaction is because
$$\frac{\mathrm d}{\mathrm dt}([\ce{A}] + [\ce{B}] + [\ce{C}]) = 0$$
and this would be an example of a *linear invariant*.


