Loss of derivatives in the infinite type

We prove hypoellipticity with loss of ϵϵ derivatives for a system of complex vector fields whose Lie-span has a superlogarithmic estimate. In CxRCxR, the model is (L¯¯¯¯,f¯¯¯kL)(L¯,f¯kL) where f¯¯¯=z¯¯¯hf¯=z¯h for h≠0h≠0 and LL is the vector field tangential to the exponentially non-degenerate hypersurface of infinite type defined by x2=e−1∣z∣αx2=e−1∣z∣α for α<1