TRS:
 {       first(0(), X) -> nil(),
  first(s(X), cons(Y)) -> cons(Y),
               from(X) -> cons(X)}
 POP* + Boolean Semantic Labelling:
  Normal positions:
  pi(from_sl=1) = [1], pi(from_sl=0) = [1], pi(first_sl=1) = [1,2], pi(first_sl=0) = [1,2]
  
Safe positions:
   pi(s_sl=1) = [1], pi(s_sl=0) = [1], pi(cons_sl=1) = [1], pi(cons_sl=0) = [1]
  
Precedence:
   first_sl=0 > nil_sl=0, 
   from_sl=0 > cons_sl=0
   empty
  
Interpretation:
   nil^(0):
    | 0
   first^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   0^(0):
    | 0
   cons^(1):
   0 | 0
   1 | 0
   s^(1):
   0 | 0
   1 | 0
   from^(1):
   0 | 0
   1 | 0
   
  
Labelling:
   nil^(0):
    | 0
   first^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   0^(0):
    | 0
   cons^(1):
   0 | 0
   1 | 0
   s^(1):
   0 | 0
   1 | 0
   from^(1):
   0 | 0
   1 | 0
   
  
Labelled predicative System:
   {              first_sl=0(0_sl=0(),X;) -> nil_sl=0(),
                  first_sl=0(0_sl=0(),X;) -> nil_sl=0(),
    first_sl=0(s_sl=0(;X),cons_sl=0(;Y);) -> cons_sl=0(;Y),
    first_sl=0(s_sl=0(;X),cons_sl=0(;Y);) -> cons_sl=0(;Y),
    first_sl=0(s_sl=0(;X),cons_sl=0(;Y);) -> cons_sl=0(;Y),
    first_sl=0(s_sl=0(;X),cons_sl=0(;Y);) -> cons_sl=0(;Y),
                            from_sl=0(X;) -> cons_sl=0(;X),
                            from_sl=0(X;) -> cons_sl=0(;X)}
  

  Qed