(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< s(X), 0, false, true >)
(SIGNATURES
    half :: [A] -> A
    if :: [A x A] -> A
    p :: [A] -> A
    ge :: [A x A] -> A
    log :: [A] -> A)
(RULES
    half(x) -> if(ge(x,s(s(0()))),x)
    if(false(),x) -> 0()
    if(true(),x) -> s(half(p(p(x))))
    p(0()) -> 0()
    p(s(x)) -> x
    ge(x,0()) -> true()
    ge(0(),s(x)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    log(0()) -> 0()
    log(s(x)) -> s(log(half(s(x)))))