  Low-mass stars are element factories that efficiently release their products
in the final stages of their evolution by means of stellar winds. Since they
are large in number, they contribute significantly to the cosmic matter cycle.
To assess this contribution quantitatively, it is crucial to obtain a detailed
picture of the stellar interior, particularly with regard to nucleosynthesis
and mixing mechanisms. We seek to benchmark stellar evolutionary models of
low-mass stars. In particular, we measure the surface abundance of ^{12}C in
thermally pulsing AGB stars with well-known mass and metallicity, which can be
used to infer information about the onset and efficiency of the third
dredge-up. We recorded high-resolution near-infrared spectra of AGB stars in
the LMC cluster NGC 1978. The sample comprised both oxygen-rich and carbon-rich
stars, and is well-constrained in terms of the stellar mass, metallicity, and
age. We derived the C/O and ^{12}C/^{13}C ratio from the target spectra by a
comparison to synthetic spectra. Then, we compared the outcomes of stellar
evolutionary models with our measurements. The M stars in NGC 1978 show values
of C/O and ^{12}C/^{13}C that can best be explained with moderate extra-mixing
on the RGB coupled to a moderate oxygen enhancement in the chemical
composition. These oxygen-rich stars do not seem to have undergone third
dredge-up episodes (yet). The C stars show carbon-to-oxygen and carbon isotopic
ratios consistent with the occurrence of the third dredge-up. We did not find S
stars in this cluster. None of the theoretical schemes that we considered was
able to reproduce the observations appropriately. Instead, we discuss some
non-standard scenarios to explain the puzzling abundance pattern in NGC 1978.
