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

  Qed