(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< s(X), 0, false, true, logError >)
(SIGNATURES
    le :: [A x A] -> A
    double :: [A] -> A
    log :: [A] -> A
    loop :: [A x A x A] -> A
    if :: [A x A x A x A] -> A)
(RULES
    le(s(x),0()) -> false()
    le(0(),y) -> true()
    le(s(x),s(y)) -> le(x,y)
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    log(0()) -> logError()
    log(s(x)) -> loop(s(x)
                     ,s(0())
                     ,0())
    loop(x,s(y),z) -> if(le(x,s(y))
                        ,x
                        ,s(y)
                        ,z)
    if(true(),x,y,z) -> z
    if(false(),x,y,z) -> loop(x
                             ,double(y)
                             ,s(z)))