  We construct a class of Gorenstein local rings $R$ which admit minimal
complete $R$-free resolutions $\bd C$ such that the sequence $\{\rank_R C_i\}$
is constant for $i< 0$, and grows exponentially for all $i>0$. Over these rings
we show that there exist finitely generated $R$-modules $M$ and $N$ such that
$\Ext^i_R(M,N)=0$ for all $i> 0$, but $\Ext^i_R(N,M)\ne 0$ for all $i>0$.
