YES
O(n^2)
TRS:
 {      g(a()) -> b(),
           a() -> g(c()),
  f(g(X), b()) -> f(a(), X)}
 DUP: We consider a non-duplicating system.
  Trs:
   {      g(a()) -> b(),
             a() -> g(c()),
    f(g(X), b()) -> f(a(), X)}
  Matrix Interpretation:
   Interpretation class: triangular
       [X3]  [X1]    [1 0][X3]   [1 1][X1]   [0]
   [f]([X2], [X0]) = [0 0][X2] + [0 0][X0] + [0]
   
         [1]
   [b] = [1]
   
         [1]
   [a] = [1]
   
         [0]
   [c] = [0]
   
       [X1]    [1 1][X1]   [0]
   [g]([X0]) = [0 1][X0] + [0]
   
   
   Qed