YES

Problem:
 app(nil(),xs) -> nil()
 app(cons(x,xs),ys) -> cons(x,app(xs,ys))

Proof:
 DP Processor:
  DPs:
   app#(cons(x,xs),ys) -> app#(xs,ys)
  TRS:
   app(nil(),xs) -> nil()
   app(cons(x,xs),ys) -> cons(x,app(xs,ys))
  KBO Processor:
   argument filtering:
    pi(nil) = []
    pi(app) = 0
    pi(cons) = [0,1]
    pi(app#) = 0
   weight function:
    w0 = 1
    w(app#) = w(app) = w(nil) = 1
    w(cons) = 0
   precedence:
    app# ~ cons ~ app ~ nil
   problem:
    DPs:
     
    TRS:
     app(nil(),xs) -> nil()
     app(cons(x,xs),ys) -> cons(x,app(xs,ys))
   Qed