(\[delN\]) – (\[delW\]) must be functions of $t$, $r$, correspondingly: $\eta^0=\eta^0(t)$, $\eta^r=\eta^r(r)$. Since ghost variables are known to compensate residual gauge transformations, it is reasonable to consider ghost solutions of the form (\[tsol\]).

Keeping in mind (\[g.c.2.1\]) and (\[tsol\]), one can rewrite Eq. (\[eLbt0\]) as $$\label{eLbt0_1}
\frac d{dt}\left[N\dot\theta^0-\frac{\partial f}{\partial V}V(\theta^r)'
   +\left(N'-\frac{\partial f}{\partial V}V'-\frac{\partial f}{\partial W}W'\right)\theta^r\right]=0.$$ As we remember, Eq. (\[d.c.11\]) is the differential form of Eq. (\[g.c.1\]). As a consequence of the latter we get $$\label{d.c.0}
N'=\frac{\partial f}{\partial V}V'+\frac{\partial f}{\partial W}W',$$ and Eq. (\[eLbt0\_1\]) looks like $$\label{eLbt0_2}
\frac d{dt}\left[N\dot\theta^0-\frac{\partial f}{\partial V}V(\theta^r)'\right]=0.$$

Under the condition (\[g.c.2.1\]) equations for ghosts $\bar\theta_0$, $\bar\theta_r$ (\[eLt0\]), (\[eLtr\]) will be reduced to $$\label{eLt0_1}
\frac d{dt}\left(\dot{\bar\theta_0}N\right)
   -\frac d{dr}\left(\dot{\bar\theta_r}\frac{N^2}{V^2}\right)=0$$ and $$\label{eLtr_1}
\frac d{dr}\left(\dot{\bar\theta_0}\frac{\partial f}{\partial V}V\right)-\ddot{\bar\theta_r}=0.$$ Again, let us consider the solutions such that $$\label{btsol}
\bar\theta^0=\bar\theta^0(t),\qquad
\bar\theta^r=\bar\theta^r(r).$$ Thus, the two equations for $\bar\theta_0$, $\bar\theta_r$ are $$\label{eLt0r_2}
\frac d{dt}\left(\dot{\bar\theta_0}N\right)=0,\qquad
\frac d{dr}\left(\dot{\bar\theta_0}\frac{\partial f}{\partial V}V\right)=0.$$

One can notice that $\pi_{N^r}$ enters into Eqs. (\[eLV\]), (\[eLW\]) being multiplied by the derivatives of the function $f^r$ which is equal to zero; $\pi_{N^r}$ also enters into Eq. (\[eLNr\]). The ghost terms are missed out from last equation if (\[tsol\]), (\[btsol\]) are true. One can put $$\label{piNr.sol}
\pi_{N^r}=0.$$ In this case Eq. (\[eLNr\]) will be reduced 