  In a prior paper the authors obtained a four-dimensional discrete integrable
dynamical system by the traveling wave reduction from the lattice super-KdV
equation in a case of finitely generated Grassmann algebra. The system is a
coupling of a Quispel-Roberts-Thompson map and a linear map but does not
satisfy the singularity confinement criterion. It was conjectured that the
dynamical degree of this system grows quadratically. In this paper,
constructing a rational variety where the system is lifted to an algebraically
stable map and using the action of the map on the Picard lattice, we prove this
conjecture. We also show that invariants can be found through the same
technique.
