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:
  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_0(2, 3) -> 1
, f_0(2, 4) -> 1
, f_0(2, 5) -> 1
, f_0(3, 2) -> 1
, f_0(3, 3) -> 1
, f_0(3, 4) -> 1
, f_0(3, 5) -> 1
, f_0(4, 2) -> 1
, f_0(4, 3) -> 1
, f_0(4, 4) -> 1
, f_0(4, 5) -> 1
, f_0(5, 2) -> 1
, f_0(5, 3) -> 1
, f_0(5, 4) -> 1
, f_0(5, 5) -> 1
, f_1(2, 7) -> 1
, f_1(3, 7) -> 1
, f_1(4, 7) -> 1
, f_1(5, 7) -> 1
, f_1(6, 6) -> 1
, f_1(6, 7) -> 1
, f_2(6, 9) -> 1
, f_2(8, 9) -> 1
, f_2(10, 12) -> 1
, f_3(10, 11) -> 1
, f_4(13, 14) -> 1
, a_0() -> 2
, a_1() -> 6
, a_2() -> 10
, a_3() -> 13
, b_0() -> 3
, b_1() -> 7
, b_2() -> 12
, s_0(2) -> 4
, s_0(3) -> 4
, s_0(4) -> 4
, s_0(5) -> 4
, s_1(6) -> 6
, s_2(10) -> 8
, s_3(13) -> 10
, c_0() -> 5
, c_1() -> 7
, c_2() -> 9
, c_3() -> 11
, c_4() -> 14 }

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