We present a detailed abundance analysis of 23 elements for a newly discovered carbon-enhanced metal-poor ( CEMP ) star , HE 0414 - 0343 , from the Chemical Abundances of Stars in the Halo ( CASH ) Project . Its spectroscopic stellar parameters are T _ { eff } = 4863 K , \log g = 1.25 , \xi = 2.20 km s ^ { -1 } , and \mbox { [ Fe / H ] } = -2.24 . Radial velocity measurements covering seven years indicate HE 0414 - 0343 to be a binary . HE 0414 - 0343 has \mbox { [ C / Fe ] } = 1.44 and is strongly enhanced in neutron-capture elements but its abundances can not be reproduced by a solar-type s-process pattern alone . Traditionally , it could be classified as “ CEMP-r/s ” star . Based on abundance comparisons with AGB star nucleosynthesis models , we suggest a new physically-motivated origin and classification scheme for CEMP-s stars and the still poorly-understood CEMP-r/s . The new scheme describes a continuous transition between these two so-far distinctly treated subgroups : CEMP-sA , CEMP-sB , and CEMP-sC . Possible causes for a continuous transition include the number of thermal pulses the AGB companion underwent , the effect of different AGB star masses on their nucleosynthetic yields , and physics that is not well approximated in 1-D stellar models such as proton ingestion episodes and rotation . Based on a set of detailed AGB models , we suggest the abundance signature of HE 0414 - 0343 to have arisen from a > 1.3 M _ { \odot } mass AGB star and a late-time mass transfer , that transformed HE 0414 - 0343 into a CEMP-sC star . We also find the [ Y/Ba ] ratio well parametrizes the classification and can thus be used to easily classify any future such stars .