  Let A be a connected graded noncommutative monomial algebra. We associate to
A a finite graph \Gamma(A) called the CPS graph of A. Finiteness properties of
the Yoneda algebra Ext_A(k,k) including Noetherianity, finite GK dimension, and
finite generation are characterized in terms of \Gamma(A). We show these
properties, notably finite generation, can be checked by means of a terminating
algorithm.
