$\Lambda$ is a finite dimensional algebra given by $$\xymatrix{1\bullet\ar@<1ex>[rr]^{\theta}\ar@<-1ex>[rr]^{\gamma}&&2\bullet\ar@(r,d)[]^{\alpha} &&&&{\rm with}\ \ \alpha^{3}=0}$$

Is $\Lambda$ is 1-syzygy finite?

$\Lambda$ is a finite dimensional algebra given by

$$\begin{array}{rcccl} 1 \rightrightarrows 2 \stackrel{\alpha}{\circlearrowright} \ \ \ \alpha^{3}=0\\ \end{array}$$

Is $\Lambda$ is 1-syzygy finite?