MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { f(x, x) -> f(0(), 1())
  , f(x, 2()) -> 2()
  , f(2(), x) -> 2()
  , 0() -> 2()
  , 1() -> 2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

Trs:
  { f(x, 2()) -> 2()
  , f(2(), x) -> 2() }

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) = [2] x1 + [2] x2 + [1]
                                       
            [0] = [0]                  
                                       
            [1] = [0]                  
                                       
            [2] = [0]                  
  
  This order satisfies the following ordering constraints:
  
      [f(x, x)] =  [4] x + [1]  
                >= [1]          
                =  [f(0(), 1())]
                                
    [f(x, 2())] =  [2] x + [1]  
                >  [0]          
                =  [2()]        
                                
    [f(2(), x)] =  [2] x + [1]  
                >  [0]          
                =  [2()]        
                                
          [0()] =  [0]          
                >= [0]          
                =  [2()]        
                                
          [1()] =  [0]          
                >= [0]          
                =  [2()]        
                                

We return to the main proof.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { f(x, x) -> f(0(), 1())
  , 0() -> 2()
  , 1() -> 2() }
Weak Trs:
  { f(x, 2()) -> 2()
  , f(2(), x) -> 2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Empty strict component of the problem is NOT empty.

Arrrr..