An example of a simple quasi-universal function in the class $\mathcal E^2$ of the Grzegorczyk hierarchy

We give an example of a quasi-universal function in the class $\mathcal E^2$ of the Grzegorczyk hierarchy. This function is of very simple structure and does not contain an explicit enumeration of any Turing machine. As a corollary we obtain a simple basis over superposition in the class $\mathcal E^2$.