Equality of pressure on a CMS and its completion

Let $(\Sigma,\sigma)$ be a finite entropy countable Markov shift, let $\rho$ be a totally bounded metric on its vertex set, and let $d$ be the corresponding metric on $\Sigma$. Write $\bar\Sigma$ for the completion of $\Sigma$, and denote by $P_\Sigma$ and $P_{\bar\Sigma}$ the corresponding pressure functions. Pressure equality conjecture. For every $\varphi\in C(\bar\Sigma,\mathbb R)$,

$$P_\Sigma(\varphi)=P_{\bar\Sigma}(\varphi).$$

This conjecture asks whether completing the shift space changes the pressure of any continuous potential. Its status is not resolved by the supplied text.