YES
O(n^4)
TRS:
 {
  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'()))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
    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'()))
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 0][X3]   [0]
       [X6]  [X2]    [0 0 0 0][X6]   [0 0 0 0][X2]   [0]
   [h]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0]
       [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 0][X0]   [0]
   
         [0]
         [0]
   [d] = [0]
         [0]
   
         [0]
         [0]
   [a] = [0]
         [0]
   
       [X11]  [X7]  [X3]    [1 0 0 0][X11]   [1 0 0 0][X7]   [1 0 0 0][X3]   [0]
       [X10]  [X6]  [X2]    [0 0 0 0][X10]   [0 0 0 0][X6]   [0 0 0 0][X2]   [0]
   [i]([ X9], [X5], [X1]) = [0 0 0 0][X9] + [0 0 0 0][X5] + [0 0 0 0][X1] + [0]
       [ X8]  [X4]  [X0]    [0 0 0 0][X8]   [0 0 0 1][X4]   [0 0 0 1][X0]   [1]
   
       [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 0][X3]   [0]
       [X6]  [X2]    [0 0 0 0][X6]   [0 0 0 0][X2]   [0]
   [g]([X5], [X1]) = [0 0 0 0][X5] + [0 0 1 0][X1] + [1]
       [X4]  [X0]    [0 0 0 1][X4]   [0 0 0 0][X0]   [1]
   
          [0]
          [0]
   [b'] = [0]
          [1]
   
          [0]
          [0]
   [d'] = [0]
          [0]
   
         [0]
         [0]
   [c] = [1]
         [0]
   
         [0]
         [0]
   [b] = [0]
         [1]
   
       [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 0][X3]   [0]
       [X6]  [X2]    [0 0 0 0][X6]   [0 0 0 0][X2]   [0]
   [.]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0]
       [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 0][X0]   [0]
   
       [X7]  [X3]    [1 0 0 1][X7]   [1 0 0 0][X3]   [0]
       [X6]  [X2]    [0 0 1 0][X6]   [0 0 0 0][X2]   [0]
   [f]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0]
       [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 0][X0]   [0]
   
         [0]
         [0]
   [e] = [0]
         [0]
   
        [X11]  [X7]  [X3]    [1 0 0 0][X11]   [1 0 0 0][X7]   [1 0 0 0][X3]   [0]
        [X10]  [X6]  [X2]    [0 0 0 0][X10]   [0 0 0 0][X6]   [0 0 0 0][X2]   [0]
   [if]([ X9], [X5], [X1]) = [0 0 0 0][X9] + [0 0 0 0][X5] + [0 0 0 0][X1] + [0]
        [ X8]  [X4]  [X0]    [0 0 0 0][X8]   [0 0 0 0][X4]   [0 0 0 0][X0]   [0]
   
   
   Qed