Calculate extreme rays of a cone

Question

Let $C=\{(y,z)\in \mathbb R^8:$

$y_1+y_3-z_1=0$,

$y_1+y_4-z_2=0$,

$y_2+y_3-z_3=0$,

$y_2+y_4-z_4=0$,

$z_1,z_2,z_3,z_4\geq 0\} $.

What is the usual technique to find the extreme rays of $C$?

Thanks.