  The planetary nebula TS 01 (also called PN G 135.9+55.9 or SBS 1150+599A),
with its record-holding low oxygen abundance and its double degenerate close
binary core (period 3.9 h), is an exceptional object located in the Galactic
halo. We have secured observational data in a complete wavelength range in
order to pin down the abundances of half a dozen elements in the nebula. The
abundances are obtained via detailed photoionization modelling taking into
account all the observational constraints (including geometry and aperture
effects) using the pseudo-3D photoionization code Cloudy_3D. The spectral
energy distribution of the ionizing radiation is taken from appropriate model
atmospheres. Both stellar components contribute to the ionization: the ``cool''
one provides the bulk of hydrogen ionization, and the ``hot'' one is
responsible for the presence of the most highly charged ions, which explains
why previous attempts to model the nebula experienced difficulties. The nebular
abundances of C, N, O, and Ne are found to be respectively, 1/3.5, 1/4.2, 1/70,
and 1/11 of the Solar value, with uncertainties of a factor 2. Thus the extreme
O deficiency of this object is confirmed. The abundances of S and Ar are less
than 1/30 of Solar. Standard models of stellar evolution and nucleosynthesis
cannot explain the abundance pattern observed in the nebula. To obtain an
extreme oxygen deficiency in a star whose progenitor has an initial mass of
about 1 msun requires an additional mixing process, which can be induced by
stellar rotation and/or by the presence of the close companion. We have
computed a stellar model with initial mass of 1 msun, appropriate metallicity,
and initial rotation of 100 kms, and find that rotation greatly improves the
agreement between the predicted and observed abundances.
