  The integrable perturbation of the degenerate boundary condition (d) by the
$\phi_{1,3}$ boundary field generates a renormalization group flow down to the
superposition of Cardy boundary states (+)&(-). Exact Thermodynamic Bethe
Ansatz (TBA) equations for all the excited states are derived here extending
the results of a previous paper to this case. As an intermediate step, the
non-Cardy boundary conformal sector (+)&(-) is also described as the scaling
limit of an A_4 lattice model with appropriate integrable boundary conditions
and produces the first example of superposition of finitized Virasoro
characters.
