YES(?,O(n^1))

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

Strict Trs:
  { h(x, c(y, z)) -> h(c(s(y), x), z)
  , h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z))) }
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.
{ h_0(2, 2) -> 1
, h_1(2, 5) -> 1
, h_1(3, 2) -> 1
, h_1(3, 5) -> 1
, h_1(9, 5) -> 1
, h_1(11, 5) -> 1
, h_2(9, 5) -> 1
, h_2(9, 7) -> 1
, h_2(11, 2) -> 1
, h_2(11, 5) -> 1
, c_0(2, 2) -> 2
, c_1(2, 2) -> 7
, c_1(2, 5) -> 7
, c_1(4, 2) -> 3
, c_1(4, 3) -> 3
, c_1(4, 11) -> 3
, c_1(6, 5) -> 5
, c_1(6, 7) -> 5
, c_2(10, 2) -> 9
, c_2(10, 3) -> 9
, c_2(10, 9) -> 9
, c_2(10, 11) -> 9
, c_2(12, 9) -> 11
, s_0(2) -> 2
, s_1(2) -> 4
, s_1(8) -> 6
, s_2(2) -> 12
, s_2(6) -> 10
, 0_0() -> 2
, 0_1() -> 8 }

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