YES(?,O(n^1))

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

Strict Trs:
  { g(c(x, s(y))) -> g(c(s(x), y))
  , f(x) -> x
  , f(c(s(x), y)) -> f(c(x, s(y)))
  , f(f(x)) -> f(d(f(x))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

Arguments of following rules are not normal-forms:

{ f(f(x)) -> f(d(f(x))) }

All above mentioned rules can be savely removed.

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

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

The problem is match-bounded by 1. The enriched problem is
compatible with the following automaton.
{ g_0(2) -> 1
, g_0(3) -> 1
, g_0(5) -> 1
, g_1(6) -> 1
, c_0(2, 2) -> 2
, c_0(2, 2) -> 4
, c_0(2, 3) -> 2
, c_0(2, 3) -> 4
, c_0(2, 5) -> 2
, c_0(2, 5) -> 4
, c_0(3, 2) -> 2
, c_0(3, 2) -> 4
, c_0(3, 3) -> 2
, c_0(3, 3) -> 4
, c_0(3, 5) -> 2
, c_0(3, 5) -> 4
, c_0(5, 2) -> 2
, c_0(5, 2) -> 4
, c_0(5, 3) -> 2
, c_0(5, 3) -> 4
, c_0(5, 5) -> 2
, c_0(5, 5) -> 4
, c_1(2, 7) -> 4
, c_1(2, 7) -> 8
, c_1(3, 7) -> 4
, c_1(3, 7) -> 8
, c_1(5, 7) -> 4
, c_1(5, 7) -> 8
, c_1(7, 2) -> 6
, c_1(7, 3) -> 6
, c_1(7, 5) -> 6
, s_0(2) -> 3
, s_0(2) -> 4
, s_0(3) -> 3
, s_0(3) -> 4
, s_0(5) -> 3
, s_0(5) -> 4
, s_1(2) -> 7
, s_1(3) -> 7
, s_1(5) -> 7
, s_1(7) -> 7
, f_0(2) -> 4
, f_0(3) -> 4
, f_0(5) -> 4
, f_1(8) -> 4
, d_0(2) -> 4
, d_0(2) -> 5
, d_0(3) -> 4
, d_0(3) -> 5
, d_0(5) -> 4
, d_0(5) -> 5
, 2 -> 4
, 3 -> 4
, 5 -> 4
, 8 -> 4 }

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