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

Strict Trs:
  { +(+(x, y), z) -> +(x, +(y, z))
  , +(*(x, y), +(*(x, z), u())) -> +(*(x, +(y, z)), u())
  , +(*(x, y), *(x, z)) -> *(x, +(y, 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.
{ +_0(2, 2) -> 1
, +_1(2, 2) -> 3
, *_0(2, 2) -> 2
, *_1(2, 3) -> 1
, *_1(2, 3) -> 3
, u_0() -> 2 }

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