(VAR m n )
(RULES 
        ack_in(0, n) -> ack_out(s(n))
        ack_in(s(m), 0) -> u11(ack_in(m, s(0)))
        u11(ack_out(n)) -> ack_out(n)
        ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m)
        u21(ack_out(n), m) -> u22(ack_in(m, n))
        u22(ack_out(n)) -> ack_out(n)
        
)