(STRATEGY
    INNERMOST)

(VAR
    X Y)
(DATATYPES
    A = µX.< true, false, n__0, n__s(X) >)
(SIGNATURES
    p :: [A] -> A
    leq :: [A x A] -> A
    if :: [A x A x A] -> A
    diff :: [A x A] -> A
    0 :: [] -> A
    s :: [A] -> A
    activate :: [A] -> A)
(RULES
    p(0()) -> 0()
    p(s(X)) -> X
    leq(0(),Y) -> true()
    leq(s(X),0()) -> false()
    leq(s(X),s(Y)) -> leq(X,Y)
    if(true(),X,Y) -> activate(X)
    if(false(),X,Y) -> activate(Y)
    diff(X,Y) -> if(leq(X,Y)
                   ,n__0()
                   ,n__s(diff(p(X),Y)))
    0() -> n__0()
    s(X) -> n__s(X)
    activate(n__0()) -> 0()
    activate(n__s(X)) -> s(X)
    activate(X) -> X)