Nei. For eksempel er $\text{gs}(\text{gs}(1,1), 3) = \frac{\frac{1+1}{2}+3}{2} = \frac{1+3}{2} = 2$, mens $\text{gs}(1, \text{gs}(1,3)) = \frac{1+\frac{1+3}{2}}{2} = \frac{1+2}{2} = 1,5$.
Generelt får vi at $\text{gs}(\text{gs}(x,y),z) = \frac{\frac{x+y}{2} + z}{2} = \frac{\frac{x+y+2z}{2}}{2} = \frac{x+y+2z}{4}$, mens $\text{gs}(x, \text{gs}(y,z)) = \frac{x + \frac{y+z}{2}}{2} = \frac{\frac{2x+y+z}{2}}{2} = \frac{2x+y+z}{4}$.