YES(O(1),O(n^1))

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

Strict Trs:
  { f(x, x) -> a()
  , f(g(x), y) -> f(x, 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:
  { f(x, x) -> a()
  , f(g(x), y) -> f(x, 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:
----------
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
    [f](x1, x2) = [1] x1 + [3] x2 + [3]
                                       
            [a] = [1]                  
                                       
        [g](x1) = [1] x1 + [3]         
  
  This order satisfies the following ordering constraints:
  
       [f(x, x)] = [4] x + [3]        
                 > [1]                
                 = [a()]              
                                      
    [f(g(x), y)] = [1] x + [3] y + [6]
                 > [1] x + [3] y + [3]
                 = [f(x, 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:
  { f(x, x) -> a()
  , f(g(x), y) -> f(x, 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))