We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).

Strict Trs:
  { double(0()) -> 0()
  , double(s(x)) -> s(s(double(x)))
  , half(double(x)) -> x
  , half(0()) -> 0()
  , half(s(0())) -> 0()
  , half(s(s(x))) -> s(half(x))
  , -(x, 0()) -> x
  , -(s(x), s(y)) -> -(x, y)
  , if(0(), y, z) -> y
  , if(s(x), y, z) -> z }
Obligation:
  runtime complexity
Answer:
  YES(?,O(n^1))

The problem is match-bounded by 1. The enriched problem is
compatible with the following automaton.
{ double_0(2) -> 1
, double_0(3) -> 1
, double_1(2) -> 8
, double_1(3) -> 8
, 0_0() -> 2
, 0_0() -> 5
, 0_0() -> 6
, 0_1() -> 1
, 0_1() -> 4
, 0_1() -> 8
, 0_1() -> 9
, s_0(2) -> 3
, s_0(2) -> 5
, s_0(2) -> 6
, s_0(3) -> 3
, s_0(3) -> 5
, s_0(3) -> 6
, s_1(7) -> 1
, s_1(7) -> 8
, s_1(8) -> 7
, s_1(9) -> 4
, s_1(9) -> 9
, half_0(2) -> 4
, half_0(3) -> 4
, half_1(2) -> 9
, half_1(3) -> 9
, -_0(2, 2) -> 5
, -_0(2, 3) -> 5
, -_0(3, 2) -> 5
, -_0(3, 3) -> 5
, -_1(2, 2) -> 5
, -_1(2, 3) -> 5
, -_1(3, 2) -> 5
, -_1(3, 3) -> 5
, if_0(2, 2, 2) -> 6
, if_0(2, 2, 3) -> 6
, if_0(2, 3, 2) -> 6
, if_0(2, 3, 3) -> 6
, if_0(3, 2, 2) -> 6
, if_0(3, 2, 3) -> 6
, if_0(3, 3, 2) -> 6
, if_0(3, 3, 3) -> 6 }

Hurray, we answered YES(?,O(n^1))