(STRATEGY
    INNERMOST)

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