YES(?,O(n^1))

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

Strict Trs:
  { c(y) -> y
  , c(c(c(y))) -> c(c(a(y, 0())))
  , c(a(a(0(), x), y)) -> a(c(c(c(0()))), y) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

Arguments of following rules are not normal-forms:

{ c(c(c(y))) -> c(c(a(y, 0()))) }

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:
  { c(y) -> y
  , c(a(a(0(), x), y)) -> a(c(c(c(0()))), 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.
{ c_0(2) -> 1
, c_0(3) -> 1
, c_1(5) -> 4
, c_1(6) -> 4
, c_1(6) -> 5
, c_1(7) -> 4
, c_1(7) -> 5
, c_1(7) -> 6
, a_0(2, 2) -> 1
, a_0(2, 2) -> 2
, a_0(2, 3) -> 1
, a_0(2, 3) -> 2
, a_0(3, 2) -> 1
, a_0(3, 2) -> 2
, a_0(3, 3) -> 1
, a_0(3, 3) -> 2
, a_1(4, 2) -> 1
, a_1(4, 3) -> 1
, 0_0() -> 1
, 0_0() -> 3
, 0_1() -> 4
, 0_1() -> 5
, 0_1() -> 6
, 0_1() -> 7
, 2 -> 1
, 3 -> 1
, 5 -> 4
, 6 -> 4
, 6 -> 5
, 7 -> 4
, 7 -> 5
, 7 -> 6 }

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