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

  Qed