YES(?,O(n^2))

Problem:
 f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
 f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))

Proof:
 Complexity Transformation Processor:
  strict:
   f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
   f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [h](x0, x1) = x0 + x1,
     
     [if](x0, x1, x2) = x0 + x1 + x2,
     
     [d'] = 0,
     
     [.](x0, x1) = x0 + x1,
     
     [e] = 0,
     
     [f](x0, x1) = x0 + x1,
     
     [d] = 0,
     
     [g](x0, x1) = x0 + x1,
     
     [c] = 0,
     
     [i](x0, x1, x2) = x0 + x1 + x2 + 1,
     
     [b'] = 0,
     
     [b] = 1,
     
     [a] = 0
    orientation:
     f(g(i(a(),b(),b'()),c()),d()) = 2 >= 1 = if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
     
     f(g(h(a(),b()),c()),d()) = 1 >= 2 = if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
    problem:
     strict:
      f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
     weak:
      f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
    Matrix Interpretation Processor:
     dimension: 2
     max_matrix:
      [1 1]
      [0 0]
      interpretation:
                     [1 0]     [1 0]  
       [h](x0, x1) = [0 0]x0 + [0 0]x1,
       
                          [1 0]     [1 0]     [1 0]  
       [if](x0, x1, x2) = [0 0]x0 + [0 0]x1 + [0 0]x2,
       
              [0]
       [d'] = [0],
       
                     [1 1]     [1 0]  
       [.](x0, x1) = [0 0]x0 + [0 0]x1,
       
             [0]
       [e] = [0],
       
                     [1 1]     [1 0]  
       [f](x0, x1) = [0 0]x0 + [0 0]x1,
       
             [0]
       [d] = [0],
       
                     [1 0]     [1 0]     [0]
       [g](x0, x1) = [0 0]x0 + [0 0]x1 + [1],
       
             [0]
       [c] = [0],
       
                         [1 0]     [1 0]     [1 0]  
       [i](x0, x1, x2) = [0 0]x0 + [0 0]x1 + [0 0]x2,
       
              [0]
       [b'] = [1],
       
             [0]
       [b] = [0],
       
             [0]
       [a] = [0]
      orientation:
                                  [1]    [0]                                                      
       f(g(h(a(),b()),c()),d()) = [0] >= [0] = if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
       
                                       [1]    [1]                                                 
       f(g(i(a(),b(),b'()),c()),d()) = [0] >= [0] = if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
      problem:
       strict:
        
       weak:
        f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
        f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
      Qed