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:
 RT 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
   interpretation:
    [*](x0, x1) = x0 + x1,
    
    [+](x0, x1) = x0 + x1 + 2
   orientation:
    +(x,+(y,z)) = x + y + z + 4 >= x + y + z + 4 = +(+(x,y),z)
    
    +(*(x,y),+(x,z)) = 2x + y + z + 4 >= x + y + z + 2 = *(x,+(y,z))
    
    +(*(x,y),+(*(x,z),u)) = u + 2x + y + z + 4 >= u + x + y + z + 4 = +(*(x,+(y,z)),u)
   problem:
    strict:
     +(x,+(y,z)) -> +(+(x,y),z)
     +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
    weak:
     +(*(x,y),+(x,z)) -> *(x,+(y,z))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [*](x0, x1) = x0 + x1 + 17,
     
     [+](x0, x1) = x0 + x1
    orientation:
     +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
     
     +(*(x,y),+(*(x,z),u)) = u + 2x + y + z + 34 >= u + x + y + z + 17 = +(*(x,+(y,z)),u)
     
     +(*(x,y),+(x,z)) = 2x + y + z + 17 >= x + y + z + 17 = *(x,+(y,z))
    problem:
     strict:
      +(x,+(y,z)) -> +(+(x,y),z)
     weak:
      +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
      +(*(x,y),+(x,z)) -> *(x,+(y,z))
    Matrix Interpretation Processor:
     dimension: 2
     interpretation:
                    [1 0]     [1 3]     [1]
      [*](x0, x1) = [0 0]x0 + [0 1]x1 + [3],
      
                         [1 3]     [5]
      [+](x0, x1) = x0 + [0 1]x1 + [1]
     orientation:
                        [1 3]    [1 6]    [13]        [1 3]    [1 3]    [10]              
      +(x,+(y,z)) = x + [0 1]y + [0 1]z + [2 ] >= x + [0 1]y + [0 1]z + [2 ] = +(+(x,y),z)
      
                              [1 6]    [2 0]    [1 3]    [1 6]    [24]    [1 3]    [1 0]    [1 3]    [1 6]    [14]                   
      +(*(x,y),+(*(x,z),u)) = [0 1]u + [0 0]x + [0 1]y + [0 1]z + [8 ] >= [0 1]u + [0 0]x + [0 1]y + [0 1]z + [5 ] = +(*(x,+(y,z)),u)
      
                         [2 3]    [1 3]    [1 6]    [14]    [1 0]    [1 3]    [1 6]    [9]              
      +(*(x,y),+(x,z)) = [0 1]x + [0 1]y + [0 1]z + [5 ] >= [0 0]x + [0 1]y + [0 1]z + [4] = *(x,+(y,z))
     problem:
      strict:
       
      weak:
       +(x,+(y,z)) -> +(+(x,y),z)
       +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
       +(*(x,y),+(x,z)) -> *(x,+(y,z))
     Qed