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