YES(?,O(n^1))

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

Strict Trs:
  { f(a()) -> f(c(a()))
  , f(a()) -> f(d(a()))
  , f(c(X)) -> X
  , f(c(a())) -> f(d(b()))
  , f(c(b())) -> f(d(a()))
  , f(d(X)) -> X
  , e(g(X)) -> e(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_1(3) -> 1
, f_2(5) -> 1
, a_0() -> 1
, a_0() -> 2
, a_1() -> 1
, a_1() -> 4
, a_2() -> 1
, a_2() -> 6
, c_0(2) -> 1
, c_0(2) -> 2
, c_1(4) -> 3
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, d_2(6) -> 5
, b_0() -> 1
, b_0() -> 2
, b_1() -> 1
, b_1() -> 4
, b_2() -> 1
, b_2() -> 6
, e_0(2) -> 1
, e_1(2) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, 2 -> 1
, 4 -> 1
, 6 -> 1 }

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