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

Strict Trs:
  { g(f(x), y) -> f(h(x, y))
  , h(x, y) -> g(x, f(y)) }
Obligation:
  runtime complexity
Answer:
  YES(O(1),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(1),O(n^1)).

Strict Trs:
  { g(f(x), y) -> f(h(x, y))
  , h(x, y) -> g(x, f(y)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.

Trs:
  { g(f(x), y) -> f(h(x, y))
  , h(x, y) -> g(x, f(y)) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  The following argument positions are usable:
    Uargs(f) = {1}
  
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
    [g](x1, x2) = [2] x1 + [1]
                              
        [f](x1) = [1] x1 + [4]
                              
    [h](x1, x2) = [2] x1 + [4]
  
  The order satisfies the following ordering constraints:
  
    [g(f(x), y)] = [2] x + [9] 
                 > [2] x + [8] 
                 = [f(h(x, y))]
                               
       [h(x, y)] = [2] x + [4] 
                 > [2] x + [1] 
                 = [g(x, f(y))]
                               

We return to the main proof.

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

Weak Trs:
  { g(f(x), y) -> f(h(x, y))
  , h(x, y) -> g(x, f(y)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

Empty rules are trivially bounded

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