(VAR x y z )
(RULES 
        O(0) -> 0
        +(0, x) -> x
        +(x, 0) -> x
        +(O(x), O(y)) -> O(+(x, y))
        +(O(x), I(y)) -> I(+(x, y))
        +(I(x), O(y)) -> I(+(x, y))
        +(I(x), I(y)) -> O(+(+(x, y), I(0)))
        +(x, +(y, z)) -> +(+(x, y), z)
        -(x, 0) -> x
        -(0, x) -> 0
        -(O(x), O(y)) -> O(-(x, y))
        -(O(x), I(y)) -> I(-(-(x, y), I(1)))
        -(I(x), O(y)) -> I(-(x, y))
        -(I(x), I(y)) -> O(-(x, y))
        not(true) -> false
        not(false) -> true
        and(x, true) -> x
        and(x, false) -> false
        if(true, x, y) -> x
        if(false, x, y) -> y
        ge(O(x), O(y)) -> ge(x, y)
        ge(O(x), I(y)) -> not(ge(y, x))
        ge(I(x), O(y)) -> ge(x, y)
        ge(I(x), I(y)) -> ge(x, y)
        ge(x, 0) -> true
        ge(0, O(x)) -> ge(0, x)
        ge(0, I(x)) -> false
        Log'(0) -> 0
        Log'(I(x)) -> +(Log'(x), I(0))
        Log'(O(x)) -> if(ge(x, I(0)), +(Log'(x), I(0)), 0)
        Log(x) -> -(Log'(x), I(0))
        Val(L(x)) -> x
        Val(N(x, l, r)) -> x
        Min(L(x)) -> x
        Min(N(x, l, r)) -> Min(l)
        Max(L(x)) -> x
        Max(N(x, l, r)) -> Max(r)
        BS(L(x)) -> true
        BS(N(x, l, r)) -> and(and(ge(x, Max(l)), ge(Min(r), x)), and(BS(l), BS(r)))
        Size(L(x)) -> I(0)
        Size(N(x, l, r)) -> +(+(Size(l), Size(r)), I(1))
        WB(L(x)) -> true
        WB(N(x, l, r)) -> and(if(ge(Size(l), Size(r)), ge(I(0), -(Size(l), Size(r))), ge(I(0), -(Size(r), Size(l)))), and(WB(l), WB(r)))
        
)