[X,Y]

ackin(0,X) -> ackout(s(X)).
ackin(s(X),0) -> u11(ackin(X,s(0))).
u11(ackout(X)) -> ackout(X).
ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X).
u21(ackout(X),Y) -> u22(ackin(Y,X)).
u22(ackout(X)) -> ackout(X).


