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)
   CDG 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:
     
    Qed