  -   $(x_0,\dots,x_{0k},0,0)$ is the same than the one whose extremity is $(x_0,\dots,x_{0k},0)$ in $\Gamma(f_{0k+0})$ augmented with 0 (loop over configurations $(x_0,\dots,x_{0k},0,0)$);  -   $(x_0,\dots,x_{0k},0,0)$ is the same than the one whose extremity is $(x_0,\dots,x_{0k},0)$ in $\Gamma(f_{0k+0})$ augmented with 0 (arc from configurations $(x_0,\dots,x_{0k},0,0)$ to configurations $(x_0,\dots,x_{0k},0,0)$);  -   $(x_0,\dots,x_{0k},0,0)$ is the same than the one whose extremity is $(x_0,\dots,x_{0k},0)$ in $\Gamma(f_{0k+0})$ augmented with 0 (loop over configurations $(x_0,\dots,x_{0k},0,0)$);  -   $(x_0,\dots,x_{0k},0,0)$ is the same than the one whose extremity is $(x_0,\dots,x_{0k},0)$ in $\Gamma(f_{0k+0})$ augmented with 0 (arc from configurations $(x_0,\dots,x_{0k},0,0)$ to configurations $(x_0,\dots,x_{0k},0,0)$)