YES
O(n^3)
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
       [X5]  [X2]    [1 0 0][X5]   [1 0 0][X2]   [0]
   [h]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
       [X3]  [X0]    [0 0 0][X3]   [0 0 0][X0]   [0]
   
         [0]
   [d] = [0]
         [0]
   
         [0]
   [a] = [0]
         [0]
   
       [X8]  [X5]  [X2]    [1 0 0][X8]   [1 0 0][X5]   [1 0 0][X2]   [0]
   [i]([X7], [X4], [X1]) = [0 0 0][X7] + [0 0 0][X4] + [0 0 0][X1] + [0]
       [X6]  [X3]  [X0]    [0 0 0][X6]   [0 0 1][X3]   [0 0 1][X0]   [1]
   
       [X5]  [X2]    [1 0 0][X5]   [1 0 0][X2]   [0]
   [g]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
       [X3]  [X0]    [0 0 1][X3]   [0 0 0][X0]   [1]
   
          [0]
   [b'] = [0]
          [1]
   
          [0]
   [d'] = [0]
          [0]
   
         [0]
   [c] = [0]
         [0]
   
         [0]
   [b] = [0]
         [1]
   
       [X5]  [X2]    [1 0 0][X5]   [1 0 0][X2]   [0]
   [.]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
       [X3]  [X0]    [0 0 0][X3]   [0 0 0][X0]   [0]
   
       [X5]  [X2]    [1 0 1][X5]   [1 0 0][X2]   [0]
   [f]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
       [X3]  [X0]    [0 0 0][X3]   [0 0 0][X0]   [1]
   
         [0]
   [e] = [0]
         [0]
   
        [X8]  [X5]  [X2]    [1 0 0][X8]   [1 0 0][X5]   [1 0 0][X2]   [0]
   [if]([X7], [X4], [X1]) = [0 0 0][X7] + [0 0 0][X4] + [0 0 0][X1] + [0]
        [X6]  [X3]  [X0]    [0 0 0][X6]   [0 0 0][X3]   [0 0 0][X0]   [0]
   
   
   Qed