A System with a Recursion Operator but One Higher Local Symmetry of the Form u_t=u_(xxx)+f(t,x,u,u_x,u_(xx))

We construct a recursion operator for the system $(u_t,v_t)=(u_4+v^2,1/5 v_4)$, for which only one local symmetry is known and we show that the action of the recursion operator on $(u_t,v_t)$ is a local function.