YES
O(n^5)
TRS:
 {f(f(x)) -> f(x),
   f(1()) -> f(g(1())),
  g(g(x)) -> g(x),
   g(0()) -> g(f(0()))}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(f(x)) -> f(x),
     f(1()) -> f(g(1())),
    g(g(x)) -> g(x),
     g(0()) -> g(f(0()))
   }
  Matrix Interpretation:
   Interpretation class: triangular
         [0]
         [0]
   [0] = [0]
         [0]
         [1]
   
         [0]
         [1]
   [1] = [1]
         [1]
         [0]
   
       [X4]    [1 0 0 0 1][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [g]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [1]
   
       [X4]    [1 0 1 1 0][X4]   [0]
       [X3]    [0 1 0 1 0][X3]   [0]
   [f]([X2]) = [0 0 0 0 0][X2] + [1]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
   
   Qed