Classification conjecture for locally complexified-gentle algebras

Let $A$ be a connected $\mathbb{R}$-algebra. An algebra is locally complexified-gentle of uniform type if it is Morita equivalent to an algebra satisfying condition (1) or (2) of Theorem 1, and it is of special type if it is Morita equivalent to an algebra satisfying condition (3) of that theorem. Classification conjecture. $A$ is locally complexified-gentle if and only if it is locally complexified-gentle either of uniform type or of special type. This conjecture proposes a complete classification of connected locally complexified-gentle algebras by the two types introduced in the paper; the source provides no resolution.