Context. A large fraction of the carbon-enhanced, extremely metal-poor halo giants ([Fe/H] < -2.5) are also strongly enriched in neutron-capture elements from the s process (CEMP-s stars). The conventional explanation for the properties of these stars is mass transfer from a nearby binary companion on the asymptotic giant branch (AGB). This scenario leads to a number of testable predictions in terms of the properties of the putative binary system and the resulting abundance pattern. Among the CEMP stars, some stars further exhibit overabundances in r-process elements on top of the s-process enrichment, and are tagged CEMP-rs stars. Although the nucleosynthesis process responsible for this kind of mixed abundance pattern is still under debate, CEMP-rs stars seem to belong to binary systems as do CEMP-s stars. Aims: Our aim is to present and analyse in detail our comprehensive data set of systematic radial-velocity measurements and high-resolution spectroscopy of the CEMP star HE 0017 0055. Methods: Our precise radial-velocity monitoring of HE 0017 0055 over 2940 days (8 yr) with the Nordic Optical Telescope and Mercator telescopes exhibits variability, with a period of 384 d and amplitude of 540 ± 27 m s-1 superimposed on a nearly linear long-term decline of ~1 m s-1 day-1. We used high-resolution HERMES/Mercator and Keck/HIRES spectra to derive elemental abundances with 1D LTE MARCS models. A metallicity of [Fe/H] ~ -2.4 is found, along with s-process overabundances of the order of 2 dex (with the exception of [Y/Fe] ~ 0.5), and most notably overabundances of r-process elements like Sm, Eu, Dy, and Er in the range 0.9-2.0 dex. With [Ba/Fe] > 1.9 dex and [Eu/Fe] = 2.3 dex, HE 0017 0055 is a CEMP-rs star. We used the derived atmospheric parameters and abundances to infer HE 0017 0055 evolutionary status from a comparison with evolutionary tracks. Results: HE 0017 0055 appears to be a giant star below the tip of the red giant branch. The s-process pollution must therefore originate from mass transfer from a companion formerly on the AGB, which is now a carbon-oxygen white dwarf (WD). If the 384 d velocity variations are attributed to the WD companion, its orbit must be seen almost face-on, with i ~ 2.3°, because the mass function is very small: f(M1,M2) = (6.1 ± 1.1) × 10-6M?. Alternatively, the WD orbital motion could be responsible for the long-term velocity variations, with a period of several decades. The 384 d variations should then be attributed either to a low-mass inner companion (perhaps a brown dwarf, depending on the orbital inclination), or to stellar pulsations. The latter possibility is made likely by the fact that similar low-amplitude velocity variations, with periods close to 1 yr, have been reported for other CEMP stars in a companion paper. A definite conclusion about the origin of the 384 d velocity variations should however await the detection of synchronous low-amplitude photometric variations. Based on observations performed with the Mercator telescope and the Nordic Optical Telescope (NOT), operated by the Nordic Optical Telescope Scientific Association at the Roque de los Muchachos Observatory, La Palma, Spain, of the Instituto de Astrofïsica de Canarias.
