  We consider the Abdesselam-Rivasseau (AR) model turning the Jacobian
Conjecture (JC) into a problem of the perturbative quantum field theory. Within
the AR model, the JC inverse map is represented by a formal integral generating
the tree's expansion for this map. By assigning colors to the edges in the
vertex of the AR model and performing selective Gaussian integration, we show
the termination of the tree's series for the inverse map. The latter implies
the correctness of JC.
