= Solution
\b[No prime and no presentation of $G_1$ have <p-deficiency> at least one.] Abelianizing the cyclic squaring relations makes each generator zero: for example $vwv^{-1}=w^2$ becomes $w=2w$, so $w=0$, and the other four relations kill $x,y,z,v$. Thus the <abelianization> of $G_1$ is trivial and $d_p(G_1)=0$ for every <prime number> $p$. The presentation-independent <p-rank of a group> bound from the general solution gives
$$
\boxed{\operatorname{def}_p(\mathcal P)\leq d_p(G_1)=0}
$$
for every <group presentation> $\mathcal P$ of $G_1$. This rules out alternative presentations, not just the one displayed.
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