Minimality conjecture for the classification of degenerate gentle two-cycle algebras

Let $\Lambda_0(p,r)$, for $p\in\mathbb{N}_+$ and $r\in[0,p-1]$, and $\Lambda_0'(p,0)$, for $p\in\mathbb{N}_+$, be the algebras in the classification of degenerate gentle two-cycle algebras. Minimality conjecture. Different algebras from this list are not derived (equivalently, tilting-cotilting) equivalent. This conjecture asserts that the classification list is minimal; the preceding theorem establishes that every degenerate gentle two-cycle algebra is equivalent to an algebra on the list, while the non-equivalence of distinct listed algebras remains conjectural in the source.