(VAR b x xs y z )
(RULES 
        times(x, y) -> sum(generate(x, y))
        generate(x, y) -> gen(x, y, 0)
        gen(x, y, z) -> if(ge(z, x), x, y, z)
        if(true, x, y, z) -> nil
        if(false, x, y, z) -> cons(y, gen(x, y, s(z)))
        sum(xs) -> sum2(xs, 0)
        sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
        ifsum(true, b, xs, y) -> y
        ifsum(false, b, xs, y) -> ifsum2(b, xs, y)
        ifsum2(true, xs, y) -> sum2(tail(xs), y)
        ifsum2(false, xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
        isNil(nil) -> true
        isNil(cons(x, xs)) -> false
        tail(nil) -> nil
        tail(cons(x, xs)) -> xs
        head(cons(x, xs)) -> x
        head(nil) -> error
        isZero(0) -> true
        isZero(s(0)) -> false
        isZero(s(s(x))) -> isZero(s(x))
        p(0) -> s(s(0))
        p(s(0)) -> 0
        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)
        a -> c
        a -> d
        
)