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

Strict Trs:
  { f(0()) -> cons(0())
  , f(s(0())) -> f(p(s(0())))
  , p(s(X)) -> X }
Obligation:
  runtime complexity
Answer:
  YES(?,O(n^1))

The input is overlay and right-linear. Switching to innermost
rewriting.

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

Strict Trs:
  { f(0()) -> cons(0())
  , f(s(0())) -> f(p(s(0())))
  , p(s(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.
{ f_0(2) -> 1
, f_0(3) -> 1
, f_0(4) -> 1
, f_1(7) -> 1
, 0_0() -> 2
, 0_0() -> 5
, 0_1() -> 6
, 0_1() -> 7
, 0_2() -> 9
, cons_0(2) -> 3
, cons_0(2) -> 5
, cons_0(3) -> 3
, cons_0(3) -> 5
, cons_0(4) -> 3
, cons_0(4) -> 5
, cons_1(6) -> 1
, cons_2(9) -> 1
, s_0(2) -> 4
, s_0(2) -> 5
, s_0(3) -> 4
, s_0(3) -> 5
, s_0(4) -> 4
, s_0(4) -> 5
, s_1(6) -> 8
, p_0(2) -> 5
, p_0(3) -> 5
, p_0(4) -> 5
, p_1(8) -> 7 }

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