YES(?,O(n^1))

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

Strict Trs:
  { +(+(x, y), z) -> +(x, +(y, z))
  , +(f(x), +(f(y), z)) -> +(f(+(x, y)), z)
  , +(f(x), f(y)) -> f(+(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.
{ +_0(2, 2) -> 1
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3 }

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