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However!! Following this result they state: "If it were possible to use the heat rejected in the process [2-3, the isochoric decompression] to be added to the cycle during process [4-1, the isochoric compression] in a reversible fashion (this is called regeneration), the resulting efficiency would be ... 1-T_l/T_h. Note that this efficiency is equal to that of a Carnot engine."
So my guess is that Carl's analysis is irreversible at some juncture, namely, the heat rejected to the cold reservoir in the isochoric decompression.