Every aperiodic function computed by a Mealy machine is computed by a composition of flip-flop Mealy machines: the implication "aperiodic $\Rightarrow$ composition of flip-flops" of Theorem A.2.8 of Transducers, the hard half. By Lemma A.2.11 the function is computed by a machine whose state transformations satisfy the stabilisation condition (); the proof of the Krohn–Rhodes theorem is then run for this machine, and every machine arising in the induction inherits (), since it only uses state transformations of the original one, so that no reversible machine with more than one state ever appears and every prime in the decomposition is a flip-flop.