YES(O(1),O(n^2))

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^2)).

Strict Trs: { f(g(x), y, y) -> g(f(x, x, y)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^2))

We use the processor 'custom shape polynomial interpretation' 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^2)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  TcT has computed the following constructor-restricted polynomial
  interpretation.
  [f](x1, x2, x3) = 1 + 2*x1 + 2*x1^2 + 2*x2 + 2*x3
                                                   
          [g](x1) = 1 + x1                         
                                                   
  
  This order satisfies the following ordering constraints.
  
    [f(g(x), y, y)] = 5 + 6*x + 2*x^2 + 4*y
                    > 2 + 4*x + 2*x^2 + 2*y
                    = [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:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

Empty rules are trivially bounded

Hurray, we answered YES(O(1),O(n^2))