TRS:
 {    +(0(), y) -> y,
     +(s(x), y) -> s(+(x, y)),
      -(0(), y) -> 0(),
      -(x, 0()) -> x,
  -(s(x), s(y)) -> -(x, y)}
 POP* + Boolean Semantic Labelling:
  Normal positions:
  pi(-_sl=1) = [1,2], pi(-_sl=0) = [1,2], pi(+_sl=1) = [1,2], pi(+_sl=0) = [1,2]
  
Safe positions:
   pi(s_sl=1) = [1], pi(s_sl=0) = [1]
  
Precedence:
   +_sl=0 > s_sl=1, 
   +_sl=1 > s_sl=0
   empty
  
Interpretation:
   +^(2):
   00 | 0
   01 | 1
   10 | 1
   11 | 1
   0^(0):
    | 0
   s^(1):
   0 | 0
   1 | 1
   -^(2):
   00 | 0
   01 | 0
   10 | 1
   11 | 0
   
  
Labelling:
   +^(2):
   00 | 1
   01 | 0
   10 | 0
   11 | 0
   0^(0):
    | 0
   s^(1):
   0 | 0
   1 | 1
   -^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   
  
Labelled predicative System:
   {           +_sl=1(0_sl=0(),y;) -> y,
               +_sl=0(0_sl=0(),y;) -> y,
             +_sl=1(s_sl=0(;x),y;) -> s_sl=0(;+_sl=1(x,y;)),
             +_sl=0(s_sl=1(;x),y;) -> s_sl=1(;+_sl=0(x,y;)),
             +_sl=0(s_sl=0(;x),y;) -> s_sl=1(;+_sl=0(x,y;)),
             +_sl=0(s_sl=1(;x),y;) -> s_sl=1(;+_sl=0(x,y;)),
               -_sl=0(0_sl=0(),y;) -> 0_sl=0(),
               -_sl=0(0_sl=0(),y;) -> 0_sl=0(),
               -_sl=0(x,0_sl=0();) -> x,
               -_sl=0(x,0_sl=0();) -> x,
    -_sl=0(s_sl=0(;x),s_sl=0(;y);) -> -_sl=0(x,y;),
    -_sl=0(s_sl=1(;x),s_sl=0(;y);) -> -_sl=0(x,y;),
    -_sl=0(s_sl=0(;x),s_sl=1(;y);) -> -_sl=0(x,y;),
    -_sl=0(s_sl=1(;x),s_sl=1(;y);) -> -_sl=0(x,y;)}
  

  Qed