TRS:
 {f(x, x) -> f(g(x), x),
     g(x) -> s(x)}
 POP* + Boolean Semantic Labelling:
  Normal positions:
  pi(g_sl=0) = [1], pi(f_sl=1) = [1,2]
  
Safe positions:
   pi(s_sl=1) = [1], pi(s_sl=0) = [1], pi(g_sl=1) = [1], pi(f_sl=0) = [1,2]
  
Precedence:
   g_sl=1 > s_sl=1, 
   g_sl=0 > s_sl=1, 
   f_sl=1 > g_sl=1, 
   f_sl=1 > g_sl=0, 
   f_sl=1 > f_sl=0
   empty
  
Interpretation:
   f^(2):
   00 | 1
   01 | 0
   10 | 1
   11 | 0
   g^(1):
   0 | 1
   1 | 0
   s^(1):
   0 | 1
   1 | 0
   
  
Labelling:
   f^(2):
   00 | 1
   01 | 0
   10 | 0
   11 | 1
   g^(1):
   0 | 1
   1 | 0
   s^(1):
   0 | 1
   1 | 1
   
  
Labelled predicative System:
   {f_sl=1(x,x;) -> f_sl=0(;g_sl=1(;x),x),
    f_sl=1(x,x;) -> f_sl=0(;g_sl=0(x;),x),
      g_sl=1(;x) -> s_sl=1(;x),
      g_sl=0(x;) -> s_sl=1(;x)}
  

  Qed