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))
  Usable Rule Processor:
   DPs:
    app#(cons(x,xs),ys) -> app#(xs,ys)
   TRS:
    
   Restore Modifier:
    DPs:
     app#(cons(x,xs),ys) -> app#(xs,ys)
    TRS:
     app(nil(),xs) -> nil()
     app(cons(x,xs),ys) -> cons(x,app(xs,ys))
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 1/1
     DPs:
      app#(cons(x,xs),ys) -> app#(xs,ys)
     TRS:
      app(nil(),xs) -> nil()
      app(cons(x,xs),ys) -> cons(x,app(xs,ys))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [app#](x0, x1) = x0,
       
       [cons](x0, x1) = x1 + 1,
       
       [app](x0, x1) = x0,
       
       [nil] = 0
      orientation:
       app#(cons(x,xs),ys) = xs + 1 >= xs = app#(xs,ys)
       
       app(nil(),xs) = 0 >= 0 = nil()
       
       app(cons(x,xs),ys) = xs + 1 >= xs + 1 = cons(x,app(xs,ys))
      problem:
       DPs:
        
       TRS:
        app(nil(),xs) -> nil()
        app(cons(x,xs),ys) -> cons(x,app(xs,ys))
      Qed