Write a description for $F(x+1,y,z)=H(z,F(x,y,z))$.
I was thinking of using composition: $\mathbf{C}(H,I_{3,3},...)$ where $I_{3,3}$ is used for the $z$ argument in $H$. But how do I finish this composition with the argument $F(x,y,z)$? Do I use identity?