Before revision:  We present a rigorous analytical treatment of the  steady-state kinetic equations including higher-order terminal effects , and then apply the results to the fidelity problem of some real DNAPs .
After revision:  We present a rigorous analytical treatment of the steady-state kinetic equations of any-order terminal effects, and derive analytical expressions for fidelity in terms of kinetic parameters under bio-relevant conditions. These expressions offer new insights on how the the higher-order terminal effects , and then apply the results to the fidelity problem of some real DNAPs .