YES(?,O(n^1))

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

Strict Trs:
  { f(X) -> if(X, c(), n__f(true()))
  , f(X) -> n__f(X)
  , if(true(), X, Y) -> X
  , if(false(), X, Y) -> activate(Y)
  , activate(X) -> X
  , activate(n__f(X)) -> f(X) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

The problem is match-bounded by 3. The enriched problem is
compatible with the following automaton.
{ f_0(2) -> 1
, f_1(2) -> 1
, f_2(5) -> 1
, f_2(8) -> 1
, if_0(2, 2, 2) -> 1
, if_1(2, 3, 4) -> 1
, if_2(2, 6, 7) -> 1
, if_3(5, 9, 10) -> 1
, if_3(8, 9, 10) -> 1
, c_0() -> 1
, c_0() -> 2
, c_1() -> 1
, c_1() -> 3
, c_2() -> 1
, c_2() -> 6
, c_3() -> 1
, c_3() -> 9
, n__f_0(2) -> 1
, n__f_0(2) -> 2
, n__f_1(2) -> 1
, n__f_1(5) -> 1
, n__f_1(5) -> 4
, n__f_2(2) -> 1
, n__f_2(8) -> 1
, n__f_2(8) -> 7
, n__f_3(5) -> 1
, n__f_3(8) -> 1
, n__f_3(11) -> 10
, true_0() -> 1
, true_0() -> 2
, true_1() -> 5
, true_2() -> 8
, true_3() -> 11
, false_0() -> 1
, false_0() -> 2
, activate_0(2) -> 1
, activate_1(2) -> 1
, activate_1(4) -> 1
, activate_1(7) -> 1
, 2 -> 1
, 3 -> 1
, 4 -> 1
, 6 -> 1
, 7 -> 1
, 9 -> 1 }

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