  We demonstrate that among the potential sources of the primordial abundance
variations of the proton-capture elements in globular-cluster stars proposed so
far, such as the hot-bottom burning in massive AGB stars and H burning in the
convective cores of supermassive and fast-rotating massive MS stars, only the
supermassive MS stars with M > 10,000 Msun can explain all the observed
abundance correlations without any fine-tuning of model parameters. We use our
assumed chemical composition for the pristine gas in M13 (NGC6205) and its
mixtures with 50% and 90% of the material partially processed in H burning in
the 60,000 Msun MS model star as the initial compositions for the normal,
intermediate and extreme populations of low-mass stars in this globular
cluster, as suggested by its O-Na anti-correlation. We evolve these stars from
the zero-age MS to the RGB tip with the thermohaline and parametric
prescriptions for the RGB extra mixing. We find that the 3He-driven
thermohaline convection cannot explain the evolutionary decline of [C/Fe] in
M13 RGB stars, which, on the other hand, is well reproduced with the universal
values for the mixing depth and rate calibrated using the observed decrease of
[C/Fe] with MV in the globular cluster NGC5466 that does not have the
primordial abundance variations.
