YES(?,O(n^2))

Problem:
 f(g(f(a()),h(a(),f(a())))) -> f(h(g(f(a()),a()),g(f(a()),f(a()))))

Proof:
 Complexity Transformation Processor:
  strict:
   f(g(f(a()),h(a(),f(a())))) -> f(h(g(f(a()),a()),g(f(a()),f(a()))))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 2
   max_matrix:
    [1 1]
    [0 0]
    interpretation:
                   [1 0]     [1 0]     [0]
     [g](x0, x1) = [0 0]x0 + [0 0]x1 + [1],
     
                   [1 0]     [1 1]     [1]
     [h](x0, x1) = [0 0]x0 + [0 0]x1 + [0],
     
               [1 1]     [0]
     [f](x0) = [0 0]x0 + [1],
     
           [0]
     [a] = [0]
    orientation:
                                  [3]    [2]                                       
     f(g(f(a()),h(a(),f(a())))) = [1] >= [1] = f(h(g(f(a()),a()),g(f(a()),f(a()))))
    problem:
     strict:
      
     weak:
      f(g(f(a()),h(a(),f(a())))) -> f(h(g(f(a()),a()),g(f(a()),f(a()))))
    Qed