\bar{\theta}) = p_{r}(t) + \theta \,(\dot{\bar R}) 
+ \bar\theta\, (\dot R) + i\,\theta\,\bar\theta (\dot S). \end{aligned}$$ In the above, we have chosen $B_1(t) = -\,\bar B_2(t) = -\,{\cal B}$ and taken the inputs from (14). The conditions (15) are now supported by the observations: $s_{d}\,(\lambda \bar C) = 0$ and $s_{ad}\,(\lambda C) = 0$. These two conditions lead to the following restrictions on the supervariables: $$\begin{aligned}
\Lambda (t, \theta, \bar\theta)\,{\bar {F}}^{(R)}(t, \theta, \bar{\theta}) = 
\lambda (t)\, \bar C (t), 
\qquad \Lambda (t, \theta, \bar\theta)\,F^{(R)}(t, \theta, \bar{\theta}) = 
\lambda (t)\, C (t).\end{aligned}$$ Finally, we obtain the expressions for the secondary variables in terms of the original variables of the Lagrangian (1) as (see, e.g. \[25\] for details): $$\bar{R} = C,\quad\qquad R = \bar{C},\qquad\quad {\cal B} = (r - a),\qquad\quad S = (r - a)\,\equiv {\cal B}.$$ The substitution of these values into the expansions (13) and (17) leads to the following [*final*]{} expressions for the expansion of the supervariables (see, e.g. \[25\] for details) $$\begin{aligned}
\Lambda^{(d)}\,(t, \theta, \bar{\theta}) &=& \lambda(t) + \theta\, (C) + \bar{\theta}\, (\bar{C}) 
 +  \theta\, \bar{\theta}\,
[i\, (r - a)] \nonumber\\
&\equiv & \lambda(t) + \theta\, (s_{ad}\, \lambda) + \bar{\theta}\,(s_{d}\, \lambda) 
+ \theta\,\bar{\theta}\, (s_{d}\,s_{ad}\,\lambda), \nonumber\\
F^{(d)}\,(t, \theta, \bar{\theta}) 