YES

Problem:
 app(id(),x) -> x
 app(plus(),0()) -> id()
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))

Proof:
 DP Processor:
  DPs:
   app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
   app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
   app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
  TRS:
   app(id(),x) -> x
   app(plus(),0()) -> id()
   app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
  EDG Processor:
   DPs:
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
   TRS:
    app(id(),x) -> x
    app(plus(),0()) -> id()
    app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
   graph:
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
   CDG Processor:
    DPs:
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    TRS:
     app(id(),x) -> x
     app(plus(),0()) -> id()
     app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    graph:
     
    Qed