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

Strict Trs: { f(s(X), Y) -> h(s(f(h(Y), X))) }
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, 2) -> 1
, f_1(5, 2) -> 4
, s_0(2) -> 2
, s_1(4) -> 3
, h_0(2) -> 2
, h_1(2) -> 5
, h_1(3) -> 1 }

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