YES

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

Proof:
 DP Processor:
  DPs:
   +#(x,s(y)) -> +#(x,y)
   +#(x,s(y)) -> s#(+(x,y))
   s#(+(0(),y)) -> s#(y)
  TRS:
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   +(0(),s(y)) -> s(y)
   s(+(0(),y)) -> s(y)
  TDG Processor:
   DPs:
    +#(x,s(y)) -> +#(x,y)
    +#(x,s(y)) -> s#(+(x,y))
    s#(+(0(),y)) -> s#(y)
   TRS:
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    +(0(),s(y)) -> s(y)
    s(+(0(),y)) -> s(y)
   graph:
    s#(+(0(),y)) -> s#(y) -> s#(+(0(),y)) -> s#(y)
    +#(x,s(y)) -> s#(+(x,y)) -> s#(+(0(),y)) -> s#(y)
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> s#(+(x,y))
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
   Restore Modifier:
    DPs:
     +#(x,s(y)) -> +#(x,y)
     +#(x,s(y)) -> s#(+(x,y))
     s#(+(0(),y)) -> s#(y)
    TRS:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     +(0(),s(y)) -> s(y)
     s(+(0(),y)) -> s(y)
    SCC Processor:
     #sccs: 2
     #rules: 2
     #arcs: 4/9
     DPs:
      +#(x,s(y)) -> +#(x,y)
     TRS:
      +(x,0()) -> x
      +(x,s(y)) -> s(+(x,y))
      +(0(),s(y)) -> s(y)
      s(+(0(),y)) -> s(y)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [+#](x0, x1) = x1 + 1,
       
       [s](x0) = x0 + 1,
       
       [+](x0, x1) = x0 + x1,
       
       [0] = 0
      orientation:
       +#(x,s(y)) = y + 2 >= y + 1 = +#(x,y)
       
       +(x,0()) = x >= x = x
       
       +(x,s(y)) = x + y + 1 >= x + y + 1 = s(+(x,y))
       
       +(0(),s(y)) = y + 1 >= y + 1 = s(y)
       
       s(+(0(),y)) = y + 1 >= y + 1 = s(y)
      problem:
       DPs:
        
       TRS:
        +(x,0()) -> x
        +(x,s(y)) -> s(+(x,y))
        +(0(),s(y)) -> s(y)
        s(+(0(),y)) -> s(y)
      Qed
     
     DPs:
      s#(+(0(),y)) -> s#(y)
     TRS:
      +(x,0()) -> x
      +(x,s(y)) -> s(+(x,y))
      +(0(),s(y)) -> s(y)
      s(+(0(),y)) -> s(y)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [s#](x0) = x0 + 1,
       
       [s](x0) = 1,
       
       [+](x0, x1) = x0 + x1,
       
       [0] = 1
      orientation:
       s#(+(0(),y)) = y + 2 >= y + 1 = s#(y)
       
       +(x,0()) = x + 1 >= x = x
       
       +(x,s(y)) = x + 1 >= 1 = s(+(x,y))
       
       +(0(),s(y)) = 2 >= 1 = s(y)
       
       s(+(0(),y)) = 1 >= 1 = s(y)
      problem:
       DPs:
        
       TRS:
        +(x,0()) -> x
        +(x,s(y)) -> s(+(x,y))
        +(0(),s(y)) -> s(y)
        s(+(0(),y)) -> s(y)
      Qed