(STRATEGY
    INNERMOST)

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