YES(?,O(n^1))

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

Strict Trs:
  { f(0()) -> s(0())
  , f(s(0())) -> s(s(0()))
  , f(s(0())) -> *(s(s(0())), f(0()))
  , f(+(x, y)) -> *(f(x), f(y))
  , f(+(x, s(0()))) -> +(s(s(0())), f(x)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

The problem is match-bounded by 2. The enriched problem is
compatible with the following automaton.
{ f_0(2) -> 1
, f_0(3) -> 1
, f_0(4) -> 1
, f_0(5) -> 1
, f_1(2) -> 1
, f_1(2) -> 7
, f_1(3) -> 7
, f_1(4) -> 7
, f_1(5) -> 7
, f_1(6) -> 7
, 0_0() -> 2
, 0_1() -> 6
, 0_2() -> 8
, s_0(2) -> 3
, s_0(3) -> 3
, s_0(4) -> 3
, s_0(5) -> 3
, s_1(1) -> 1
, s_1(6) -> 1
, s_1(6) -> 7
, s_1(7) -> 7
, s_2(8) -> 7
, *_0(2, 2) -> 4
, *_0(2, 3) -> 4
, *_0(2, 4) -> 4
, *_0(2, 5) -> 4
, *_0(3, 2) -> 4
, *_0(3, 3) -> 4
, *_0(3, 4) -> 4
, *_0(3, 5) -> 4
, *_0(4, 2) -> 4
, *_0(4, 3) -> 4
, *_0(4, 4) -> 4
, *_0(4, 5) -> 4
, *_0(5, 2) -> 4
, *_0(5, 3) -> 4
, *_0(5, 4) -> 4
, *_0(5, 5) -> 4
, *_1(1, 7) -> 1
, *_1(7, 7) -> 1
, *_1(7, 7) -> 7
, +_0(2, 2) -> 5
, +_0(2, 3) -> 5
, +_0(2, 4) -> 5
, +_0(2, 5) -> 5
, +_0(3, 2) -> 5
, +_0(3, 3) -> 5
, +_0(3, 4) -> 5
, +_0(3, 5) -> 5
, +_0(4, 2) -> 5
, +_0(4, 3) -> 5
, +_0(4, 4) -> 5
, +_0(4, 5) -> 5
, +_0(5, 2) -> 5
, +_0(5, 3) -> 5
, +_0(5, 4) -> 5
, +_0(5, 5) -> 5
, +_1(1, 7) -> 1
, +_1(1, 7) -> 7 }

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