  The origin of Carbon Enhanced Metal-Poor (CEMP-no) stars with low abundances
of neutron-capture elements is still unclear. These stars are ubiquitous, found
primarily in the Milky Way halo and ultra-faint dwarf galaxies (UFDs). To make
a major step forward, we developed a data-calibrated model for B\"ootes I that
simultaneously includes all carbon sources: supernovae and asymptotic giant
branch (AGB) stars both from first (Pop III) stars, and subsequent normal star
formation (Pop II). We demonstrate that each of these sources leave a specific
chemical signature in the gas, allowing us to identify the origin of present
day CEMP-no stars through their location in the A(C)-[Fe/H] diagram. The CEMP
stars with A(C)>6 are predominantly enriched by AGB Pop II stars. We identify a
new class of 'moderate CEMP-s' stars with A(C)~ 7 and 0<[Ba/Fe]<+1 , imprinted
by winds from AGB stars. True Pop III descendants are predicted to have A(C)<6
and a constant [C/Mg] with [Fe/H], in perfect agreement with observations in
B\"ootes I and the Milky Way halo. For the first time we now have a complete
picture of the origins of CEMP-no stars which can and will be verified with
future observations.
