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

Strict Trs:
  { c(c(x)) -> b(c(b(c(x))))
  , c(c(b(c(x)))) -> b(a(0(), c(x)))
  , a(0(), x) -> c(c(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.
{ c_0(2) -> 1
, c_0(4) -> 1
, c_1(2) -> 5
, c_1(4) -> 5
, c_1(5) -> 3
, c_2(2) -> 8
, c_2(4) -> 8
, c_2(7) -> 6
, b_0(2) -> 2
, b_0(4) -> 2
, b_2(6) -> 3
, b_2(8) -> 7
, a_0(2, 2) -> 3
, a_0(2, 4) -> 3
, a_0(4, 2) -> 3
, a_0(4, 4) -> 3
, 0_0() -> 4 }

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