$\tau$-Tilting Finite Algebras With Nonempty Left Or Right Parts Are Representation-Finite

Let $\mathrm{\Lambda }$ be a finite dimensional algebra such that ${\mathcal{L}}_{\mathrm{\Lambda }}$ or ${\mathcal{R}}_{\mathrm{\Lambda }}\mathrm{\ne }\mathrm{\varnothing }$. Then $\mathrm{\Lambda }$ is $\tau$-tilting finite if and only if $\mathrm{\Lambda }$ is representation-finite.