YES(?,O(n^2))

Problem:
 f(a(),b()) -> f(a(),c())
 f(c(),d()) -> f(b(),d())

Proof:
 Complexity Transformation Processor:
  strict:
   f(a(),b()) -> f(a(),c())
   f(c(),d()) -> f(b(),d())
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [d] = 0,
     
     [c] = 1,
     
     [f](x0, x1) = x0 + x1,
     
     [b] = 0,
     
     [a] = 0
    orientation:
     f(a(),b()) = 0 >= 1 = f(a(),c())
     
     f(c(),d()) = 1 >= 0 = f(b(),d())
    problem:
     strict:
      f(a(),b()) -> f(a(),c())
     weak:
      f(c(),d()) -> f(b(),d())
    Matrix Interpretation Processor:
     dimension: 2
     max_matrix:
      [1 1]
      [0 0]
      interpretation:
             [0]
       [d] = [0],
       
             [0]
       [c] = [0],
       
                     [1 0]     [1 1]  
       [f](x0, x1) = [0 0]x0 + [0 0]x1,
       
             [0]
       [b] = [1],
       
             [0]
       [a] = [0]
      orientation:
                    [1]    [0]             
       f(a(),b()) = [0] >= [0] = f(a(),c())
       
                    [0]    [0]             
       f(c(),d()) = [0] >= [0] = f(b(),d())
      problem:
       strict:
        
       weak:
        f(a(),b()) -> f(a(),c())
        f(c(),d()) -> f(b(),d())
      Qed