(STRATEGY
    INNERMOST)

(VAR
    b x y)
(DATATYPES
    A = µX.< 0, s(X), true, false, logZeroError, g, h >)
(SIGNATURES
    half :: [A] -> A
    le :: [A x A] -> A
    inc :: [A] -> A
    logarithm :: [A] -> A
    logIter :: [A x A] -> A
    if :: [A x A x A x A] -> A
    f :: [] -> 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(s(x)) -> s(inc(x))
    inc(0()) -> s(0())
    logarithm(x) -> logIter(x,0())
    logIter(x,y) -> if(le(s(0()),x)
                      ,le(s(s(0())),x)
                      ,half(x)
                      ,inc(y))
    if(false(),b,x,y) ->
      logZeroError()
    if(true(),false(),x,s(y)) -> y
    if(true(),true(),x,y) ->
      logIter(x,y)
    f() -> g()
    f() -> h())