(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, s(X), true, false >)
(SIGNATURES
    minus :: [A x A] -> A
    mod :: [A x A] -> A
    if :: [A x A x A] -> A
    gcd :: [A x A] -> A
    lt :: [A x A] -> A)
(RULES
    minus(0(),x) -> 0()
    minus(s(x),0()) -> s(x)
    minus(s(x),s(y)) -> minus(x,y)
    mod(x,0()) -> 0()
    mod(x,s(y)) -> if(lt(x,s(y))
                     ,x
                     ,s(y))
    if(true(),x,y) -> x
    if(false(),x,y) -> mod(minus(x
                                ,y)
                          ,y)
    gcd(x,0()) -> x
    gcd(0(),s(y)) -> s(y)
    gcd(s(x),s(y)) -> gcd(mod(s(x)
                             ,s(y))
                         ,mod(s(y),s(x)))
    lt(x,0()) -> false()
    lt(0(),s(x)) -> true()
    lt(s(x),s(y)) -> lt(x,y))