(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, true, cons(X, X), s(X), false, nil >)
(SIGNATURES
    numbers :: [] -> A
    d :: [A] -> A
    if :: [A x A] -> A
    le :: [A x A] -> A
    nr :: [] -> A
    ack :: [A x A] -> A)
(RULES
    numbers() -> d(0())
    d(x) -> if(le(x,nr()),x)
    if(true(),x) -> cons(x,d(s(x)))
    if(false(),x) -> nil()
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    nr() ->
      ack(s(s(s(s(s(s(0())))))),0())
    ack(0(),x) -> s(x)
    ack(s(x),0()) -> ack(x,s(0()))
    ack(s(x),s(y)) -> ack(x
                         ,ack(s(x),y)))