YES(?,O(n^1))

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

Strict Trs:
  { f(a(), a()) -> f(a(), b())
  , f(a(), b()) -> f(s(a()), c())
  , f(s(X), c()) -> f(X, c())
  , f(c(), c()) -> f(a(), a()) }
Obligation:
  runtime complexity
Answer:
  YES(?,O(n^1))

The input is overlay and right-linear. Switching to innermost
rewriting.

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

Strict Trs:
  { f(a(), a()) -> f(a(), b())
  , f(a(), b()) -> f(s(a()), c())
  , f(s(X), c()) -> f(X, c())
  , f(c(), c()) -> f(a(), a()) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

The problem is match-bounded by 4. The enriched problem is
compatible with the following automaton.
{ f_0(2, 2) -> 1
, f_1(2, 4) -> 1
, f_1(3, 3) -> 1
, f_1(3, 4) -> 1
, f_2(3, 6) -> 1
, f_2(5, 6) -> 1
, f_2(7, 9) -> 1
, f_3(7, 8) -> 1
, f_4(10, 11) -> 1
, a_0() -> 2
, a_1() -> 3
, a_2() -> 7
, a_3() -> 10
, b_0() -> 2
, b_1() -> 4
, b_2() -> 9
, s_0(2) -> 2
, s_1(3) -> 3
, s_2(7) -> 5
, s_3(10) -> 7
, c_0() -> 2
, c_1() -> 4
, c_2() -> 6
, c_3() -> 8
, c_4() -> 11 }

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