YES(?,O(n^1))

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

Strict Trs:
  { f(a()) -> g(h(a()))
  , h(g(x)) -> g(h(f(x)))
  , k(x, h(x), a()) -> h(x)
  , k(f(x), y, x) -> 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_1(2) -> 9
, f_1(3) -> 9
, f_2(6) -> 11
, a_0() -> 2
, a_1() -> 7
, g_0(2) -> 3
, g_0(3) -> 3
, g_1(6) -> 1
, g_1(6) -> 9
, g_1(8) -> 4
, g_2(10) -> 8
, h_0(2) -> 4
, h_0(3) -> 4
, h_1(7) -> 6
, h_1(9) -> 8
, h_2(11) -> 10
, k_0(2, 2, 2) -> 5
, k_0(2, 2, 3) -> 5
, k_0(2, 3, 2) -> 5
, k_0(2, 3, 3) -> 5
, k_0(3, 2, 2) -> 5
, k_0(3, 2, 3) -> 5
, k_0(3, 3, 2) -> 5
, k_0(3, 3, 3) -> 5 }

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