YES(?,O(n^2))

Problem:
 +(x,+(y,z)) -> +(+(x,y),z)
 +(*(x,y),+(x,z)) -> *(x,+(y,z))
 +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)

Proof:
 Complexity Transformation Processor:
  strict:
   +(x,+(y,z)) -> +(+(x,y),z)
   +(*(x,y),+(x,z)) -> *(x,+(y,z))
   +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [*](x0, x1) = x0 + x1 + 1,
     
     [+](x0, x1) = x0 + x1
    orientation:
     +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
     
     +(*(x,y),+(x,z)) = 2x + y + z + 1 >= x + y + z + 1 = *(x,+(y,z))
     
     +(*(x,y),+(*(x,z),u)) = u + 2x + y + z + 2 >= u + x + y + z + 1 = +(*(x,+(y,z)),u)
    problem:
     strict:
      +(x,+(y,z)) -> +(+(x,y),z)
      +(*(x,y),+(x,z)) -> *(x,+(y,z))
     weak:
      +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [*](x0, x1) = x0 + x1,
       
       [+](x0, x1) = x0 + x1 + 1
      orientation:
       +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
       
       +(*(x,y),+(x,z)) = 2x + y + z + 2 >= x + y + z + 1 = *(x,+(y,z))
       
       +(*(x,y),+(*(x,z),u)) = u + 2x + y + z + 2 >= u + x + y + z + 2 = +(*(x,+(y,z)),u)
      problem:
       strict:
        +(x,+(y,z)) -> +(+(x,y),z)
       weak:
        +(*(x,y),+(x,z)) -> *(x,+(y,z))
        +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
      Matrix Interpretation Processor:
       dimension: 2
       max_matrix:
        [1 1]
        [0 1]
        interpretation:
                       [1 0]     [1 1]  
         [*](x0, x1) = [0 0]x0 + [0 1]x1,
         
                            [1 1]     [0]
         [+](x0, x1) = x0 + [0 1]x1 + [1]
        orientation:
                           [1 1]    [1 2]    [1]        [1 1]    [1 1]    [0]              
         +(x,+(y,z)) = x + [0 1]y + [0 1]z + [2] >= x + [0 1]y + [0 1]z + [2] = +(+(x,y),z)
         
                            [2 1]    [1 1]    [1 2]    [1]    [1 0]    [1 1]    [1 2]    [1]              
         +(*(x,y),+(x,z)) = [0 1]x + [0 1]y + [0 1]z + [2] >= [0 0]x + [0 1]y + [0 1]z + [1] = *(x,+(y,z))
         
                                 [1 2]    [2 0]    [1 1]    [1 2]    [1]    [1 1]    [1 0]    [1 1]    [1 2]    [1]                   
         +(*(x,y),+(*(x,z),u)) = [0 1]u + [0 0]x + [0 1]y + [0 1]z + [2] >= [0 1]u + [0 0]x + [0 1]y + [0 1]z + [2] = +(*(x,+(y,z)),u)
        problem:
         strict:
          
         weak:
          +(x,+(y,z)) -> +(+(x,y),z)
          +(*(x,y),+(x,z)) -> *(x,+(y,z))
          +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
        Qed