YES

Problem:
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 -(0(),y) -> 0()
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)

Proof:
 DP Processor:
  DPs:
   +#(s(x),y) -> +#(x,y)
   -#(s(x),s(y)) -> -#(x,y)
  TRS:
   +(0(),y) -> y
   +(s(x),y) -> s(+(x,y))
   -(0(),y) -> 0()
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
  Usable Rule Processor:
   DPs:
    +#(s(x),y) -> +#(x,y)
    -#(s(x),s(y)) -> -#(x,y)
   TRS:
    
   ADG Processor:
    DPs:
     +#(s(x),y) -> +#(x,y)
     -#(s(x),s(y)) -> -#(x,y)
    TRS:
     
    graph:
     -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
     +#(s(x),y) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
    Restore Modifier:
     DPs:
      +#(s(x),y) -> +#(x,y)
      -#(s(x),s(y)) -> -#(x,y)
     TRS:
      +(0(),y) -> y
      +(s(x),y) -> s(+(x,y))
      -(0(),y) -> 0()
      -(x,0()) -> x
      -(s(x),s(y)) -> -(x,y)
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 2/4
      DPs:
       +#(s(x),y) -> +#(x,y)
      TRS:
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [+#](x0, x1) = x0 + 1,
        
        [-](x0, x1) = x0,
        
        [s](x0) = x0 + 1,
        
        [+](x0, x1) = x0 + x1,
        
        [0] = 0
       orientation:
        +#(s(x),y) = x + 2 >= x + 1 = +#(x,y)
        
        +(0(),y) = y >= y = y
        
        +(s(x),y) = x + y + 1 >= x + y + 1 = s(+(x,y))
        
        -(0(),y) = 0 >= 0 = 0()
        
        -(x,0()) = x >= x = x
        
        -(s(x),s(y)) = x + 1 >= x = -(x,y)
       problem:
        DPs:
         
        TRS:
         +(0(),y) -> y
         +(s(x),y) -> s(+(x,y))
         -(0(),y) -> 0()
         -(x,0()) -> x
         -(s(x),s(y)) -> -(x,y)
       Qed
      
      DPs:
       -#(s(x),s(y)) -> -#(x,y)
      TRS:
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [-#](x0, x1) = x0,
        
        [-](x0, x1) = x0,
        
        [s](x0) = x0 + 1,
        
        [+](x0, x1) = x0 + x1,
        
        [0] = 0
       orientation:
        -#(s(x),s(y)) = x + 1 >= x = -#(x,y)
        
        +(0(),y) = y >= y = y
        
        +(s(x),y) = x + y + 1 >= x + y + 1 = s(+(x,y))
        
        -(0(),y) = 0 >= 0 = 0()
        
        -(x,0()) = x >= x = x
        
        -(s(x),s(y)) = x + 1 >= x = -(x,y)
       problem:
        DPs:
         
        TRS:
         +(0(),y) -> y
         +(s(x),y) -> s(+(x,y))
         -(0(),y) -> 0()
         -(x,0()) -> x
         -(s(x),s(y)) -> -(x,y)
       Qed