(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, s(X), true, false >)
(SIGNATURES
    half :: [A] -> A
    le :: [A x A] -> A
    inc :: [A] -> A
    log :: [A] -> A
    log2 :: [A x A] -> A
    if :: [A x A x A] -> A)
(RULES
    half(0()) -> 0()
    half(s(0())) -> 0()
    half(s(s(x))) -> s(half(x))
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    inc(0()) -> 0()
    inc(s(x)) -> s(inc(x))
    log(x) -> log2(x,0())
    log2(x,y) -> if(le(x,s(0()))
                   ,x
                   ,inc(y))
    if(true(),x,s(y)) -> y
    if(false(),x,y) -> log2(half(x)
                           ,y))