YES(?,O(n^1))

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

Strict Trs:
  { f(x, x, y) -> x
  , f(x, y, y) -> y
  , f(x, y, g(y)) -> x
  , f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))
  , f(g(x), x, y) -> y }
Obligation:
  runtime complexity
Answer:
  YES(?,O(n^1))

The problem is match-bounded by 0. The enriched problem is
compatible with the following automaton.
{ f_0(2, 2, 2) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, 2 -> 1 }

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