.  [**Part 0. $G_0 \cap G_0 = \emptyset$.**]{} Let $(i_0,0,k_0,m_0,0,\dots,0) \in \mathcal G_0$, $(i_0,j_0,k_0,0,0,\dots,0,0,0,\dots,0) \in \mathcal G_0$ and suppose that $$i_0q^0+k_0q+m_0(q^0+0)=i_0q^0+j_0+k_0q+