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))
  KBO Processor:
   argument filtering:
    pi(id) = []
    pi(app) = [0,1]
    pi(plus) = []
    pi(0) = []
    pi(s) = []
    pi(app#) = 0
   usable rules:
    app(id(),x) -> x
    app(plus(),0()) -> id()
    app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
   weight function:
    w0 = 1
    w(app#) = w(s) = w(0) = w(plus) = w(id) = 1
    w(app) = 0
   precedence:
    app# ~ s ~ 0 ~ plus ~ app ~ id
   problem:
    DPs:
     
    TRS:
     app(id(),x) -> x
     app(plus(),0()) -> id()
     app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
   Qed