(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, s(X), true, false >)
(SIGNATURES
    half :: [A] -> A
    inc :: [A] -> A
    zero :: [A] -> A
    p :: [A] -> A
    bits :: [A] -> A
    bitIter :: [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))
    inc(0()) -> 0()
    inc(s(x)) -> s(inc(x))
    zero(0()) -> true()
    zero(s(x)) -> false()
    p(0()) -> 0()
    p(s(x)) -> x
    bits(x) -> bitIter(x,0())
    bitIter(x,y) -> if(zero(x)
                      ,x
                      ,inc(y))
    if(true(),x,y) -> p(y)
    if(false(),x,y) ->
      bitIter(half(x),y))