A representation-directed algebra $A$ over a field $K$ has the property that for every indecomposable module $M$ we have $End_A(M) \cong k$ and $Ext_A^i(M,M)=0$ for all $i>0$.

Question: In case for every indecomposable module $M$ we have $End_A(M) \cong k$ and $Ext_A^i(M,M)=0$ for all $i>0$, is $A$ representation-directed? Is it true under the additional assumption that $A$ is representation-finite?