  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.
