  Within the minimum model of neutron stars (NS) consisting of neutrons,
protons and electrons, a new approach is proposed for inferring the symmetry
energy of super-dense neutron-rich nucleonic matter above twice the saturation
density $\rho_0$ of nuclear matter directly from integrating iteratively
barotropic pressures in both neutron stars and heavy-ion reactions.
Simultaneously, the proton fraction of NSs at $\beta$ equilibrium is extracted
as a function of baryon density from the same procedure. An application of this
approach using the NS pressure from GW170817 and the pressure in cold symmetric
nuclear matter (SNM) extracted earlier by analyzing nuclear collective flow
data in relativistic heavy-ion collisions provides a useful constraining band
for the symmetry energy above $2\rho_0$.
