(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< 0, s(X) >)
(SIGNATURES
    double :: [A] -> A
    half :: [A] -> A
    - :: [A x A] -> A
    if :: [A x A x A] -> A)
(RULES
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    half(0()) -> 0()
    half(s(0())) -> 0()
    half(s(s(x))) -> s(half(x))
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
    if(0(),y,z) -> y
    if(s(x),y,z) -> z
    half(double(x)) -> x)