We reconsider the possibility that gamma-ray bursts (GRBs) are the sources of the ultra-high energy cosmic
rays (UHECRs) within the internal shock model, assuming a pure proton composition of the UHECRs.
For the first time, we combine the information from gamma-rays, cosmic rays, prompt neutrinos, and
cosmogenic neutrinos quantitatively in a joint cosmic ray production and propagation model, and we
show that the information on the cosmic energy budget can be obtained as a consequence. In addition
to the neutron model, we consider alternative scenarios for the cosmic ray escape from the GRBs, i.e., that
cosmic rays can leak from the sources. We find that the dip model, which describes the ankle in UHECR
observations by the pair production dip, is strongly disfavored in combination with the internal shock
model because (a) unrealistically high baryonic loadings (energy in protons versus energy in electrons/
gamma-rays) are needed for the individual GRBs and (b) the prompt neutrino flux easily overshoots
the corresponding neutrino bound. On the other hand, GRBs may account for the UHECRs in the ankle
transition model if cosmic rays leak out from the source at the highest energies. In that case, we demonstrate
that future neutrino observations can efficiently test most of the parameter space – unless the
baryonic loading is much larger than previously anticipated