(STRATEGY
    INNERMOST)

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