&=& C(t) + \theta\, (0) + \bar{\theta}\, [i\,(r - a)]  
+  \theta\, \bar{\theta}\, (0) \nonumber\\
&\equiv & C(t) + \theta\, (s_{ad}\, C) + \bar{\theta}\,(s_{d}\, C) 
+ \theta\,\bar{\theta}\, (s_{d}\,s_{ad}\,C), \nonumber\\
{\bar F}^{(d)}\,(t, \theta, \bar{\theta}) &=& \bar{C}(t) + \theta\, [-\,i\,(r - a)] 
+ \bar{\theta}\,(0)  +  \theta\, \bar{\theta}\, (0) \nonumber\\
&\equiv & \bar{C}(t) + \theta\, (s_{ad}\, \bar{C}) + \bar{\theta}\,(s_{d}\, \bar{C}) 
+ \theta\,\bar{\theta}\, (s_{d}\,s_{ad}\,\bar{C}),\nonumber\\
P^{(d)}_{r}(t, \theta, \bar{\theta}) &=& p_{r}(t) + \theta\, (\dot{C}) 
+ \bar{\theta}\, (\dot{\bar{C}}) 
+ \theta\,\bar{\theta}\, (i \dot r)\nonumber\\
& \equiv & p_{r}(t) + \theta\,(s_{ad}\,p_{r}) + \bar{\theta}\, (s_{d}\,p_{r}) 
+ \theta\,\bar{\theta}\,(s_{d}\,s_{ad}\,p_{r}),\end{aligned}$$ where the superscript $(d)$ on the supervariables denotes the expansions that have been obtained after the application of DHC and DGIRs. A careful and close look at the above expansions demonstrate that we have already obtained the non-trival (anti-)co-BRST symmetry transformations for the variables ($\lambda, C, \bar C, p_{r}$) of the 1$D$ rigid rotor. The trivial nilpotent (anti-)co-BRST symmetry transformations $s_{(a)d} [r, p_{\theta}, \theta] = 0$ are self-evident. It is clear that there is a geometrical meaning of $s_{(a)d}$ in the language of translational operators ($\partial_\theta, \partial_{\bar\theta}$) along the Grassmannian directions ($\theta, \bar\theta$) of the (1, 2)-dimensional supermanifold. The nilpotency (${\partial_\theta}^2 = {\partial_{\bar\theta}}^2 = 0$) and absolute anticommutativity ($\partial_\theta \,\partial_{\bar\theta} +\partial_{\bar\theta}\,\partial_\theta$) of these 