(STRATEGY
    INNERMOST)

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