formalism the BRST transformations for our model are given by (\[delN\]) – (\[delW\]), where infinitesimal parameters $\eta^{\mu}$ should be replaced by $\bar\varepsilon\theta^{\mu}$, $\bar\varepsilon$ is a Grassmannian parameter, $$\begin{aligned}
\label{delN1}
\delta N&=&\bar\varepsilon\left[-\dot N\theta^0-N'\theta^r-N\dot\theta^0+N N^r(\theta^0)'\right];\\
\label{delNr1}
\delta N^r&=&\bar\varepsilon\left[-\dot N^r\theta^0-(N^r)'\theta^r-N^r\dot\theta^0-\dot\theta^r
   +N^r(\theta^r)'+\frac{N^2}{V^2}(\theta^0)'+(N^r)^2(\theta^0)'\right];\\
\label{delV1}
\delta V&=&\bar\varepsilon\left[-\dot V\theta^0-V'\theta^r-V(\theta^r)'-V N^r(\theta^0)'\right];\\
\label{delW1}
\delta W&=&\bar\varepsilon\left[-\dot W\theta^0-W'\theta^r\right].\end{aligned}$$ Moreover, $$\begin{aligned}
\label{delt0}
\delta\theta^0&=&\bar\varepsilon\left[\dot\theta^0\theta^0+(\theta^0)'\theta^r\right];\\
\label{deltr}
\delta\theta^r&=&\bar\varepsilon\left[\dot\theta^r\theta^0+(\theta^r)'\theta^r\right];\\
\label{delbt0}
\delta\bar\theta_0&=&-\bar\varepsilon\lambda_0;\\
\label{delbtr}
\delta\bar\theta_r&=&-\bar\varepsilon\lambda_r;\\
\label{dell0}
\delta\lambda_0&=&0;\\
\label{dellr}
\delta\lambda_r&=&0.\end{aligned}$$ The transformations (\[delN1\]) – (\[dellr\]) should be supplemented by coordinated transformations $$\label{coord.tr}
\delta t=\bar\varepsilon\theta^0;\qquad
\delta r=\bar\varepsilon\theta^r.$$ As a consequence of a global symmetry there exists a BRST charge which plays a role of a generator of BRST transformations in extended phase space. As we have already mentioned, in the BFV approach it is constructed as a series in powers of Grassmannian variables with coefficients given by generalized structure functions of constraints algebra: $$\label{gen_BFV}
\Omega=c^{\alpha}U^{(0)}_{\alpha}
 +c^{\beta}c^{\gamma}U^{(1)\alpha}_{\gamma\beta}\bar\rho_{\alpha}+\ldots$$ $c^{\alpha}$, $\bar\rho_{\alpha}$ are BFV ghosts, $U^{(n)}$ are $n$th order structure functions, while zero order structure functions $U^{(0)}_{\alpha}$ are Dirac secondary constraints.

Since the BFV prescription of constructing the BRST charge is essentially rely upon constraints algebra, it cannot produce correct transformations for gauge gravitational variables, like a linear combination of constraints cannot produce them in the Dirac approach. In [@Shest1] we have analyzed the 