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

Strict Trs:
  { walk#1(Nil()) -> walk_xs()
  , walk#1(Cons(x4, x3)) -> comp_f_g(walk#1(x3), walk_xs_3(x4))
  , comp_f_g#1(walk_xs(), walk_xs_3(x8), x12) -> Cons(x8, x12)
  , comp_f_g#1(comp_f_g(x7, x9), walk_xs_3(x8), x12) ->
    comp_f_g#1(x7, x9, Cons(x8, x12))
  , main(Nil()) -> Nil()
  , main(Cons(x4, x5)) ->
    comp_f_g#1(walk#1(x5), walk_xs_3(x4), Nil()) }
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.
{ walk#1_0(2) -> 1
, walk#1_1(2) -> 3
, Nil_0() -> 2
, Nil_1() -> 1
, walk_xs_0() -> 2
, walk_xs_1() -> 1
, walk_xs_1() -> 3
, Cons_0(2, 2) -> 2
, Cons_1(2, 1) -> 1
, Cons_1(2, 2) -> 1
, Cons_2(2, 1) -> 1
, comp_f_g_0(2, 2) -> 2
, comp_f_g_1(3, 4) -> 1
, comp_f_g_1(3, 4) -> 3
, walk_xs_3_0(2) -> 2
, walk_xs_3_1(2) -> 4
, comp_f_g#1_0(2, 2, 2) -> 1
, comp_f_g#1_1(2, 2, 1) -> 1
, comp_f_g#1_1(3, 4, 1) -> 1
, comp_f_g#1_2(3, 4, 1) -> 1
, main_0(2) -> 1 }

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