Jacobian conjecture for mappings of a special type in ${\mathbb C}^2$

We show that a polynomial mapping of the type $ (x \rightarrow F[x+f(a(x)+b(y))],\, y \rightarrow G[y+g(c(x)+d(y))])$, where $(a,b,c,d,f,g,F,G)$ are polynomials with non-zero Jacobian is a composition of no more than 3 linear or triangular transformations. This result, however, leaves the possibility of existence of a counterexample of polynomial complexity two.