(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
isEmpty(cons(x, xs)) → false
isEmpty(nil) → true
isZero(0) → true
isZero(s(x)) → false
head(cons(x, xs)) → x
tail(cons(x, xs)) → xs
tail(nil) → nil
p(s(s(x))) → s(p(s(x)))
p(s(0)) → 0
p(0) → 0
inc(s(x)) → s(inc(x))
inc(0) → s(0)
sumList(xs, y) → if(isEmpty(xs), isZero(head(xs)), y, tail(xs), cons(p(head(xs)), tail(xs)), inc(y))
if(true, b, y, xs, ys, x) → y
if(false, true, y, xs, ys, x) → sumList(xs, y)
if(false, false, y, xs, ys, x) → sumList(ys, x)
sum(xs) → sumList(xs, 0)
Q is empty.