Total specific energy (E/m) vs the z-th component of the specific angular momentum (L_z/m) for the Ret-II and r stars. The colours represent the time evolution of Ret-II from the past (blue) to today (red) based on a numerical simulation with N = 960k. The symbols (filled circle, unfilled square, and filled rhombus) represent the different types of r stars (r-I, r-II, and r-lim). For each individual r star, we generated ten random realisations inside their ± σ error box. Block (1) comprises the stars presented in Table A.1 as the ‘most probable’ candidates, overlapping in the E/m vs. L_z/m phase-space with the present-day Ret-II. Block (2)+(3) represents the stars with the moderate ‘tentative’ and low ‘in question’ probabilities.