YES

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

Proof:
 DP Processor:
  DPs:
   +#(s(x),s(y)) -> +#(y,0())
   +#(s(x),s(y)) -> +#(s(x),+(y,0()))
  TRS:
   +(0(),y) -> y
   +(s(x),0()) -> s(x)
   +(s(x),s(y)) -> s(+(s(x),+(y,0())))
  Usable Rule Processor:
   DPs:
    +#(s(x),s(y)) -> +#(y,0())
    +#(s(x),s(y)) -> +#(s(x),+(y,0()))
   TRS:
    +(0(),y) -> y
    +(s(x),0()) -> s(x)
   EDG Processor:
    DPs:
     +#(s(x),s(y)) -> +#(y,0())
     +#(s(x),s(y)) -> +#(s(x),+(y,0()))
    TRS:
     +(0(),y) -> y
     +(s(x),0()) -> s(x)
    graph:
     +#(s(x),s(y)) -> +#(s(x),+(y,0())) ->
     +#(s(x),s(y)) -> +#(y,0())
     +#(s(x),s(y)) -> +#(s(x),+(y,0())) -> +#(s(x),s(y)) -> +#(s(x),+(y,0()))
    Restore Modifier:
     DPs:
      +#(s(x),s(y)) -> +#(y,0())
      +#(s(x),s(y)) -> +#(s(x),+(y,0()))
     TRS:
      +(0(),y) -> y
      +(s(x),0()) -> s(x)
      +(s(x),s(y)) -> s(+(s(x),+(y,0())))
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 2/4
      DPs:
       +#(s(x),s(y)) -> +#(s(x),+(y,0()))
      TRS:
       +(0(),y) -> y
       +(s(x),0()) -> s(x)
       +(s(x),s(y)) -> s(+(s(x),+(y,0())))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [+#](x0, x1) = x0 + x1 + 1,
        
        [s](x0) = x0 + 1,
        
        [+](x0, x1) = x0 + x1,
        
        [0] = 0
       orientation:
        +#(s(x),s(y)) = x + y + 3 >= x + y + 2 = +#(s(x),+(y,0()))
        
        +(0(),y) = y >= y = y
        
        +(s(x),0()) = x + 1 >= x + 1 = s(x)
        
        +(s(x),s(y)) = x + y + 2 >= x + y + 2 = s(+(s(x),+(y,0())))
       problem:
        DPs:
         
        TRS:
         +(0(),y) -> y
         +(s(x),0()) -> s(x)
         +(s(x),s(y)) -> s(+(s(x),+(y,0())))
       Qed