YES(?,O(n^2))

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

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