Illustration of quantities used for qualitative analysis using one example. Left panel: ejected cosmic ray spectrum as a function of (observer’s frame) energy. Right panel: ejected composition ⟨ln A⟩ as a function of (observer’s frame) energy. Here adiabatic losses are taken into account, but no interactions in CMB and EBL. The left panel illustrates how to determine the spectral index, the right panel the composition at E_max and the transition energy E_trans. The maximum energy E_max is determined by acceleration and loss processes.