YES(?,O(n^1))

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

Strict Trs:
  { f(f(X)) -> f(a(b(f(X))))
  , f(a(g(X))) -> b(X)
  , b(X) -> a(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.
{ f_0(2) -> 1
, f_0(4) -> 1
, a_0(2) -> 2
, a_0(4) -> 2
, a_1(2) -> 3
, a_1(4) -> 3
, a_2(2) -> 1
, a_2(4) -> 1
, b_0(2) -> 3
, b_0(4) -> 3
, b_1(2) -> 1
, b_1(4) -> 1
, g_0(2) -> 4
, g_0(4) -> 4 }

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