YES(?,O(n^2))

Problem:
 div(X,e()) -> i(X)
 i(div(X,Y)) -> div(Y,X)
 div(div(X,Y),Z) -> div(Y,div(i(X),Z))

Proof:
 Complexity Transformation Processor:
  strict:
   div(X,e()) -> i(X)
   i(div(X,Y)) -> div(Y,X)
   div(div(X,Y),Z) -> div(Y,div(i(X),Z))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [i](x0) = x0 + 1,
     
     [div](x0, x1) = x0 + x1,
     
     [e] = 0
    orientation:
     div(X,e()) = X >= X + 1 = i(X)
     
     i(div(X,Y)) = X + Y + 1 >= X + Y = div(Y,X)
     
     div(div(X,Y),Z) = X + Y + Z >= X + Y + Z + 1 = div(Y,div(i(X),Z))
    problem:
     strict:
      div(X,e()) -> i(X)
      div(div(X,Y),Z) -> div(Y,div(i(X),Z))
     weak:
      i(div(X,Y)) -> div(Y,X)
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [i](x0) = x0,
       
       [div](x0, x1) = x0 + x1,
       
       [e] = 1
      orientation:
       div(X,e()) = X + 1 >= X = i(X)
       
       div(div(X,Y),Z) = X + Y + Z >= X + Y + Z = div(Y,div(i(X),Z))
       
       i(div(X,Y)) = X + Y >= X + Y = div(Y,X)
      problem:
       strict:
        div(div(X,Y),Z) -> div(Y,div(i(X),Z))
       weak:
        div(X,e()) -> i(X)
        i(div(X,Y)) -> div(Y,X)
      Matrix Interpretation Processor:
       dimension: 2
       max_matrix:
        [1 1]
        [0 1]
        interpretation:
                   [1 1]  
         [i](x0) = [0 1]x0,
         
                         [1 1]          [0]
         [div](x0, x1) = [0 1]x0 + x1 + [1],
         
               [0]
         [e] = [0]
        orientation:
                           [1 2]    [1 1]        [1]    [1 2]    [1 1]        [0]                     
         div(div(X,Y),Z) = [0 1]X + [0 1]Y + Z + [2] >= [0 1]X + [0 1]Y + Z + [2] = div(Y,div(i(X),Z))
         
                      [1 1]    [0]    [1 1]        
         div(X,e()) = [0 1]X + [1] >= [0 1]X = i(X)
         
                       [1 2]    [1 1]    [1]        [1 1]    [0]           
         i(div(X,Y)) = [0 1]X + [0 1]Y + [1] >= X + [0 1]Y + [1] = div(Y,X)
        problem:
         strict:
          
         weak:
          div(div(X,Y),Z) -> div(Y,div(i(X),Z))
          div(X,e()) -> i(X)
          i(div(X,Y)) -> div(Y,X)
        Qed