TRS:
 {   f(0()) -> cons(0()),
  f(s(0())) -> f(p(s(0()))),
    p(s(X)) -> X}
 POP* + Boolean Semantic Labelling:
  Normal positions:
  pi(p_sl=1) = [1], pi(p_sl=0) = [1], pi(f_sl=0) = [1]
  
Safe positions:
   pi(s_sl=1) = [1], pi(s_sl=0) = [1], pi(f_sl=1) = [1], pi(cons_sl=1) = [1], pi(cons_sl=0) = [1]
  
Precedence:
   f_sl=0 > p_sl=0, 
   f_sl=0 > f_sl=1, 
   f_sl=1 > cons_sl=0
   empty
  
Interpretation:
   cons^(1):
   0 | 0
   1 | 0
   0^(0):
    | 1
   f^(1):
   0 | 0
   1 | 0
   p^(1):
   0 | 1
   1 | 0
   s^(1):
   0 | 1
   1 | 0
   
  
Labelling:
   cons^(1):
   0 | 0
   1 | 0
   0^(0):
    | 0
   f^(1):
   0 | 0
   1 | 1
   p^(1):
   0 | 0
   1 | 0
   s^(1):
   0 | 0
   1 | 0
   
  
Labelled predicative System:
   {         f_sl=1(;0_sl=0()) -> cons_sl=0(;0_sl=0()),
    f_sl=0(s_sl=0(;0_sl=0());) -> f_sl=1(;p_sl=0(s_sl=0(;0_sl=0());)),
           p_sl=0(s_sl=0(;X);) -> X,
           p_sl=0(s_sl=0(;X);) -> X}
  

  Qed