are not of the type $T_1$. The term $T_2$ produces additional divergences that cannot be absorbed, so we have to ignore it. The $T_3$ term does not cancel any of the terms present in the action (\[Sincompfields\]). Additionally, it produces new divergent terms. However these terms might look like, they can never cancel all the divergences in (\[2pointAll\]) as divergences proportional to $K^{m}_{\ a}K^{*n}_{\ b}$ will remain. This analysis forces us to conclude that even with a non-minimal deformation our model remains nonrenormalizable.

Let us make a remark about the nonrenormalization theorem and its modifications in the case of deformed SUSY. One easily sees that the divergent terms of the effective action (\[2pointAll\]) can be rewritten as $$\Gamma^{(2)}_1\bigg|_{d.p.} = \int {\mbox{d}}^4 x_1 \hspace{1mm} {\mbox{d}}^4 x_2\hspace{1mm} {\mbox{d}}^2 \theta {\mbox{d}}^2 \bar{\theta}\hspace{1mm}
G_2(x_1, x_2, U_{(1)}, U_{(2)}) f_1(x_1, \theta, \bar{\theta}) f_2(x_2, \theta, \bar{\theta}),
\label{NRTh}$$ with $f_i = f_i (\Phi, \Phi^+, D\Phi, \bar{D}\Phi, D\Phi^+, \bar{D}\Phi^+,\dots)$. The nonlocal term in (\[NRTh\]) appears as a consequence of nonlocality in the classical action (\[SGaction\]). The result (\[NRTh\]) confirms the modified nonrenormalization theorem [@Penati]. The appearance of the spurion fields in (\[NRTh\]) signals breaking of the undeformed SUSY. In our case, symmetry which remains after the breaking is the 