(VAR i x y z )
(RULES 
        plus(x, y) -> ifPlus(isZero(x), x, inc(y))
        ifPlus(true, x, y) -> p(y)
        ifPlus(false, x, y) -> plus(p(x), y)
        times(x, y) -> timesIter(0, x, y, 0)
        timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z)
        ifTimes(true, i, x, y, z) -> z
        ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y))
        isZero(0) -> true
        isZero(s(0)) -> false
        isZero(s(s(x))) -> isZero(s(x))
        inc(0) -> s(0)
        inc(s(x)) -> s(inc(x))
        inc(x) -> s(x)
        p(0) -> 0
        p(s(x)) -> x
        p(s(s(x))) -> s(p(s(x)))
        ge(x, 0) -> true
        ge(0, s(y)) -> false
        ge(s(x), s(y)) -> ge(x, y)
        f0(0, y, x) -> f1(x, y, x)
        f1(x, y, z) -> f2(x, y, z)
        f2(x, 1, z) -> f0(x, z, z)
        f0(x, y, z) -> d
        f1(x, y, z) -> c
        
)