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)
  TDG 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)
   graph:
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
    +#(s(x),y) -> +#(x,y) -> +#(s(x),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)
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 0
     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)
    Subterm Criterion Processor:
     simple projection:
      pi(-#) = 1
     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