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

  Qed