An easy way to see that the algebra is of infinite representation type (for any $m \geq 2$) is to observe that it is a string algebra, and that you have strings of arbitrary length $(\alpha \beta \gamma^{-1})^t$, $t \geq 1$, each corresponding to an indecomposable module.

An easy way to see that the algebra is of infinite representation type (for any $m \geq 2$) is to observe that it is a string algebra, and that you have strings of arbitrary length, each corresponding to an indecomposable module.

For instance the strings $(\alpha \beta \gamma^{-1})^t$, $t \geq 1$, correspond to indecomposable modules of vector space dimension $3t+1$.