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

Strict Trs:
  { f(s(X)) -> f(X)
  , g(cons(s(X), Y)) -> s(X)
  , g(cons(0(), Y)) -> g(Y)
  , h(cons(X, Y)) -> h(g(cons(X, 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.
{ f_0(2) -> 1
, f_0(4) -> 1
, f_0(5) -> 1
, f_1(2) -> 1
, f_1(4) -> 1
, f_1(5) -> 1
, s_0(2) -> 2
, s_0(4) -> 2
, s_0(5) -> 2
, s_1(2) -> 3
, s_1(2) -> 7
, s_1(4) -> 3
, s_1(4) -> 7
, s_1(5) -> 3
, s_1(5) -> 7
, g_0(2) -> 3
, g_0(4) -> 3
, g_0(5) -> 3
, g_1(2) -> 3
, g_1(2) -> 7
, g_1(4) -> 3
, g_1(4) -> 7
, g_1(5) -> 3
, g_1(5) -> 7
, g_1(8) -> 7
, cons_0(2, 2) -> 4
, cons_0(2, 4) -> 4
, cons_0(2, 5) -> 4
, cons_0(4, 2) -> 4
, cons_0(4, 4) -> 4
, cons_0(4, 5) -> 4
, cons_0(5, 2) -> 4
, cons_0(5, 4) -> 4
, cons_0(5, 5) -> 4
, cons_1(2, 2) -> 8
, cons_1(2, 4) -> 8
, cons_1(2, 5) -> 8
, cons_1(4, 2) -> 8
, cons_1(4, 4) -> 8
, cons_1(4, 5) -> 8
, cons_1(5, 2) -> 8
, cons_1(5, 4) -> 8
, cons_1(5, 5) -> 8
, 0_0() -> 5
, h_0(2) -> 6
, h_0(4) -> 6
, h_0(5) -> 6
, h_1(7) -> 6 }

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