the adsorption eventually stops at all $i\in\M$ where $x_i=0$, that is $$\sup_{t\ge 0}\xi_i(t)=\infty \mbox{ if and only if } x_i>0.$$ Additionally, if the initial configuration is empty, then for each $x_i=0$ we must have that [**both**]{} $x_{i-1}>0$ [**and**]{} $x_{i+1}>0$.

    M                                                               Limiting configurations (up to rotation)                                                             No. of limits
  ------ -------------------------------------------------------------------------------------------------------------------------------------------------------------- ----------------
   $4$                                                              [$\left(\frac 12,0,\frac 12,0\right)$]{}                                                                   2
   $5$                                  [ $\left(\frac 14,\frac 14,0,\frac 12,0\right)$, $\left(\frac 12,0,0,\frac 12,0\right)^{*}$ ]{}                                  5 (10${}^{*}$)
   $6$                                                        [$\left(\frac 13,0,\frac 13,0,\frac 13,0\right)$ ]{}                                                             2
   $7$                         [ $\left(\frac 16,\frac16,0,\frac 13,0,\frac 13,0\right)$, $\left(\frac 13,0,\frac13,0,\frac 13,0,0\right)^{*}$]{}                        7 (14${}^{*}$)
   $8$                                                  [ $\left(\frac 14,0,\frac14,0,\frac 14,0,\frac  14,0\right)$,]{}                                                 2 (18${}^{*}$)
                           [ $\left(\frac 16,\frac 16,0,\frac13,0,0,\frac 13,0\right)^{*}$, $\left(0,0,\frac 13,0,0,\frac 13,0,\frac13\right)^{*}$]{}                   
   $9$             [ $\left(\frac 18,\frac18,0,\frac 14,0,\frac 14,0,\frac 14,0\right)$, $\left(0,0,\frac 14,0,\frac 14,0,\frac 14,0,\frac14\right)^{*}$ ]{}             9 (18${}^{*}$)
   $10$     [$\left(\frac 18,\frac18,0,\frac 14,0,\frac 18,\frac 18,0,\frac 14,0\right)$, $\left(\frac 15,0,\frac 15,0,\frac 15,0,\frac 15,0,\frac 15,0\right)$,]{}      7 (42${}^{*}$)
          [ $\left(0,\frac 14,0,0,\frac 14,0,\frac 14,0,\frac 18,\frac 18\right)^{*}$, $\left(0,\frac 14,0,\frac 14,0,0,\frac 14,0,\frac 18,\frac   14\right)^{*}$,]{}  
                [ $\left(0,0,\frac 14,0,0,\frac 14,0,\frac 14,0,\frac    14\right)^{*}$, $\left(0,0,\frac 14,0,\frac 14,0,0,\frac 14,0,\frac 14\right)^{*}$ ]{}         

  : Limiting configurations for symmetric interaction

\[Tabl2\]

         M                11               12               13                14                15                16
  ---------------- ---------------- ---------------- ----------------- ----------------- ----------------- -----------------
   Distinct conf.    1(4${}^{*}$)     2(7${}^{*}$)     1(8${}^{*}$)      3($12{}^{*}$)     2(16${}^{*}$)     3(20${}^{*}$)
     All conf.      11(44${}^{*}$)   14(74${}^{*}$)   13(104${}^{*}$)   23(142${}^{*}$)   20(220${}^{*}$)   34(290${}^{*}$)

  : Numbers of limiting configurations for symmetric 