YES(?,O(n^1))
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()}
  RLAB:
   Strict:
    {
       f(f) f(f) x -> f(f) x,
       f(f) f(g) x -> f(g) x,
       f(f) f(1) x -> f(1) x,
       f(f) f(0) x -> f(0) x,
     f(1) 1() -> f(g) g(1) 1(),
       g(g) g(f) x -> g(f) x,
       g(g) g(g) x -> g(g) x,
       g(g) g(1) x -> g(1) x,
       g(g) g(0) x -> g(0) x,
     g(0) 0() -> g(f) f(0) 0()
    }
   Weak:
    {}
   Natural interpretation:
    Strict:
     {
        f(f) f(f) x -> f(f) x,
        f(f) f(g) x -> f(g) x,
        f(f) f(1) x -> f(1) x,
        f(f) f(0) x -> f(0) x,
      f(1) 1() -> f(g) g(1) 1(),
        g(g) g(f) x -> g(f) x,
        g(g) g(g) x -> g(g) x,
        g(g) g(1) x -> g(1) x,
        g(g) g(0) x -> g(0) x,
      g(0) 0() -> g(f) f(0) 0()
     }
    Weak:
     {}
    Interpretation class: stronglylinear
    [0] = + 0
    [1] = + 6
    [g(3)](X0) = + 1*X0 + 1
    [g(2)](X0) = + 1*X0 + 2
    [g(1)](X0) = + 1*X0 + 6
    [g(0)](X0) = + 1*X0 + 0
    [f(3)](X0) = + 1*X0 + 0
    [f(2)](X0) = + 1*X0 + 7
    [f(1)](X0) = + 1*X0 + 0
    [f(0)](X0) = + 1*X0 + 4
    
    Qed