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

Strict Trs: { f(g(x), y, y) -> g(f(x, x, y)) }
Obligation:
  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(g(x), y, y) -> g(f(x, 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:
----------
  The following argument positions are usable:
    Uargs(g) = {1}
  
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
    [f](x1, x2, x3) = [2] x1 + [0]
                                  
            [g](x1) = [1] x1 + [4]
  
  The order satisfies the following ordering constraints:
  
    [f(g(x), y, y)] = [2] x + [8]    
                    > [2] x + [4]    
                    = [g(f(x, 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(g(x), y, y) -> g(f(x, x, y)) }
Obligation:
  runtime complexity
Answer:
  YES(O(1),O(1))

Empty rules are trivially bounded

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