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We investigate the well accepted idea that anomalous cosmic ray (ACR) ions originate from suprathermal halo ions by means of diffusive shock acceleration. Usually the seed ions are taken to be the interplanetary pick-up ions, but here we want to enlarge this idea by taking in addition as seed candidates also into account normal solar wind ions which according to our recent calculations are reflected from the termination shock into the upstream solar wind flow and then are also picked-up as suprathermal ions. We start out from an ideally planar shock approximation and fix the ACR spectrum by absolute spectral intensities and maximum ACR energies, taking a precalculated fraction of the suprathermal ion flow as ACR injection rate. Comparison of our calculated spectral intensities with ACR measurements near 94 AU, shows that satisfying data fits only can be achieved, if about three percent of the suprathermal ions swept into the shock structure enter into the Fermi-1 acceleration process. We also show that the spectral slope of the ACR spectra is decreasing and the spectral intensities are increasing with increasing shock compression ratios. As maximum energies available from an ideally operating diffusive Fermi-1 acceleration process we find, depending on the shock compression ratio, ion energies ranging from a few MeV up to 10<sup>3</sup> MeV. Compared to observations this seems to be a little on the high side and may point to the fact that injection into Fermi-1 acceleration near the termination shock is occurring only sporadically due to variable upstream magnetic field orientations with respect to the shock normal vector, i.e. due to variations of the obliquity of the local shock surface with respect to the local upstream magnetic field.