(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, true, s(X), false, divByZeroError >)
(SIGNATURES
    ge :: [A x A] -> A
    minus :: [A x A] -> A
    plus :: [A x A] -> A
    div :: [A x A] -> A
    ify :: [A x A x A] -> A
    if :: [A x A x A] -> A)
(RULES
    ge(0(),0()) -> true()
    ge(s(x),0()) -> ge(x,0())
    ge(0(),s(0())) -> false()
    ge(0(),s(s(x))) -> ge(0(),s(x))
    ge(s(x),s(y)) -> ge(x,y)
    minus(0(),0()) -> 0()
    minus(0(),s(x)) -> minus(0(),x)
    minus(s(x),0()) -> s(minus(x
                              ,0()))
    minus(s(x),s(y)) -> minus(x,y)
    plus(0(),0()) -> 0()
    plus(0(),s(x)) -> s(plus(0(),x))
    plus(s(x),y) -> s(plus(x,y))
    div(x,y) -> ify(ge(y,s(0()))
                   ,x
                   ,y)
    ify(false(),x,y) ->
      divByZeroError()
    ify(true(),x,y) -> if(ge(x,y)
                         ,x
                         ,y)
    if(false(),x,y) -> 0()
    if(true(),x,y) -> s(div(minus(x
                                 ,y)
                           ,y)))