(VAR x y xs)
(RULES

double(0) -> 0
double(s(x)) -> s(s(double(x)))

del(x, nil) -> nil
del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs)

if(true, x, y, xs) -> xs
if(false, x, y, xs) -> cons(y, del(x, xs))

eq(0, 0) -> true
eq(0, s(y)) -> false
eq(s(x), 0) -> false
eq(s(x), s(y)) -> eq(x, y)

first(nil) -> 0
first(cons(x, xs)) -> x

doublelist(nil) -> nil
doublelist(cons(x, xs)) -> cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs))))
)