YES(?,O(n^1))

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

Strict Trs:
  { active(f(x)) -> mark(f(f(x)))
  , f(active(x)) -> active(f(x))
  , f(mark(x)) -> mark(f(x))
  , f(no(x)) -> no(f(x))
  , chk(no(f(x))) ->
    f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))), x)))
  , chk(no(c())) -> active(c())
  , mat(f(x), f(y())) -> f(mat(x, y()))
  , mat(f(x), c()) -> no(c())
  , tp(mark(x)) ->
    tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))), 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.
{ active_0(2) -> 1
, active_1(4) -> 1
, active_2(18) -> 5
, f_0(2) -> 1
, f_1(2) -> 3
, f_1(8) -> 7
, f_1(9) -> 8
, f_1(10) -> 9
, f_1(11) -> 10
, f_1(12) -> 11
, f_1(13) -> 12
, f_1(14) -> 13
, f_1(15) -> 14
, f_1(16) -> 15
, f_1(17) -> 16
, mark_0(2) -> 2
, mark_1(3) -> 1
, mark_1(3) -> 3
, chk_0(2) -> 1
, chk_1(6) -> 5
, no_0(2) -> 2
, no_1(3) -> 1
, no_1(3) -> 3
, no_1(4) -> 6
, mat_0(2, 2) -> 1
, mat_1(7, 2) -> 6
, X_0() -> 2
, X_1() -> 17
, y_0() -> 2
, c_0() -> 2
, c_1() -> 4
, c_2() -> 18
, tp_0(2) -> 1
, tp_1(5) -> 1 }

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