The indecomposable-real-element conjecture for superunitary regions

Let $\mathcal{A}$ be a cluster algebra with a good basis $\mathfrak{B}$, and let $\mathfrak{B}_{ir}$ be the subset of indecomposable real elements, where an element $b$ is real if $b^2\in\mathfrak{B}$ and indecomposable if every factorization $b=cd$ with $c,d\in\mathfrak{B}$ has an invertible factor. For $b\in\mathfrak{B}$, write $f_b$ for its associated function. The indecomposable-real-element conjecture. The $\mathfrak{B}$-superunitary region is the subset of $\mathcal{A}(\mathbb{R}_{>0})$ on which $f_b\geq1$ for every $b\in\mathfrak{B}_{ir}$:

$$\mathcal{A}_{\mathfrak{B}}(\mathbb{R}_{\geq1})=\{p\in\mathcal{A}(\mathbb{R}_{>0})\mid f_b(p)\geq1\text{ for every }b\in\mathfrak{B}_{ir}\}.$$

This would imply equality with the ordinary superunitary region whenever the indecomposable real elements are precisely the cluster variables. The supplied text gives no resolution.