(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< true, s(X), false, 0 >)
(SIGNATURES
    minus :: [A x A] -> A
    if :: [A x A x A] -> A
    p :: [A] -> A
    ge :: [A x A] -> A
    gt :: [A x A] -> A
    div :: [A x A] -> A
    if1 :: [A x A x A] -> A
    if2 :: [A x A x A] -> A)
(RULES
    minus(x,y) -> if(gt(x,y),x,y)
    if(true(),x,y) -> s(minus(p(x)
                             ,y))
    if(false(),x,y) -> 0()
    p(0()) -> 0()
    p(s(x)) -> x
    ge(x,0()) -> true()
    ge(0(),s(x)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    gt(0(),y) -> false()
    gt(s(x),0()) -> true()
    gt(s(x),s(y)) -> gt(x,y)
    div(x,y) -> if1(ge(x,y),x,y)
    if1(true(),x,y) -> if2(gt(y,0())
                          ,x
                          ,y)
    if1(false(),x,y) -> 0()
    if2(true(),x,y) -> s(div(minus(x
                                  ,y)
                            ,y))
    if2(false(),x,y) -> 0())