(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, s(X) >)
(SIGNATURES
    min :: [A x A] -> A
    max :: [A x A] -> A
    + :: [A x A] -> A
    - :: [A x A] -> A
    * :: [A x A] -> A
    f :: [A] -> A)
(RULES
    min(0(),y) -> 0()
    min(x,0()) -> 0()
    min(s(x),s(y)) -> s(min(x,y))
    max(0(),y) -> y
    max(x,0()) -> x
    max(s(x),s(y)) -> s(max(x,y))
    +(0(),y) -> y
    +(s(x),y) -> s(+(x,y))
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
    *(x,0()) -> 0()
    *(x,s(y)) -> +(x,*(x,y))
    f(s(x)) -> f(-(max(*(s(x),s(x))
                      ,+(s(x),s(s(s(0())))))
                  ,max(s(*(s(x),s(x)))
                      ,+(s(x),s(s(s(s(0())))))))))