(VAR m n x y z )
(RULES 
        average(x, y) -> if(ge(x, y), x, y)
        if(true, x, y) -> averIter(y, x, y)
        if(false, x, y) -> averIter(x, y, x)
        averIter(x, y, z) -> ifIter(ge(x, y), x, y, z)
        ifIter(true, x, y, z) -> z
        ifIter(false, x, y, z) -> averIter(plus(x, s(s(s(0)))), plus(y, s(0)), plus(z, s(0)))
        append(nil, y) -> y
        append(cons(n, x), y) -> cons(n, app(x, y))
        low(n, nil) -> nil
        low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x))
        if_low(false, n, cons(m, x)) -> cons(m, low(n, x))
        if_low(true, n, cons(m, x)) -> low(n, x)
        high(n, nil) -> nil
        high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x))
        if_high(false, n, cons(m, x)) -> high(n, x)
        if_high(true, n, cons(m, x)) -> cons(average(m, m), high(n, x))
        quicksort(x) -> ifquick(isempty(x), x)
        ifquick(true, x) -> nil
        ifquick(false, x) -> append(quicksort(low(head(x), tail(x))), cons(tail(x), quicksort(high(head(x), tail(x)))))
        plus(0, y) -> y
        plus(s(x), y) -> s(plus(x, y))
        isempty(nil) -> true
        isempty(cons(n, x)) -> false
        head(nil) -> error
        head(cons(n, x)) -> n
        tail(nil) -> nil
        tail(cons(n, x)) -> x
        ge(x, 0) -> true
        ge(0, s(y)) -> false
        ge(s(x), s(y)) -> ge(x, y)
        a -> b
        a -> c
        
)