YES

Problem:
 app(nil(),y) -> y
 app(add(n,x),y) -> add(n,app(x,y))
 reverse(nil()) -> nil()
 reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
 shuffle(nil()) -> nil()
 shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))

Proof:
 DP Processor:
  DPs:
   app#(add(n,x),y) -> app#(x,y)
   reverse#(add(n,x)) -> reverse#(x)
   reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
   shuffle#(add(n,x)) -> reverse#(x)
   shuffle#(add(n,x)) -> shuffle#(reverse(x))
  TRS:
   app(nil(),y) -> y
   app(add(n,x),y) -> add(n,app(x,y))
   reverse(nil()) -> nil()
   reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
   shuffle(nil()) -> nil()
   shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
  Usable Rule Processor:
   DPs:
    app#(add(n,x),y) -> app#(x,y)
    reverse#(add(n,x)) -> reverse#(x)
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
    shuffle#(add(n,x)) -> reverse#(x)
    shuffle#(add(n,x)) -> shuffle#(reverse(x))
   TRS:
    reverse(nil()) -> nil()
    reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
    app(nil(),y) -> y
    app(add(n,x),y) -> add(n,app(x,y))
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
    interpretation:
     [shuffle#](x0) = x0,
     
     [reverse#](x0) = x0 + 3,
     
     [app#](x0, x1) = x0 + 4,
     
     [reverse](x0) = x0,
     
     [add](x0, x1) = x1 + 4,
     
     [app](x0, x1) = x0 + x1,
     
     [nil] = 0
    orientation:
     app#(add(n,x),y) = x + 8 >= x + 4 = app#(x,y)
     
     reverse#(add(n,x)) = x + 7 >= x + 3 = reverse#(x)
     
     reverse#(add(n,x)) = x + 7 >= x + 4 = app#(reverse(x),add(n,nil()))
     
     shuffle#(add(n,x)) = x + 4 >= x + 3 = reverse#(x)
     
     shuffle#(add(n,x)) = x + 4 >= x = shuffle#(reverse(x))
     
     reverse(nil()) = 0 >= 0 = nil()
     
     reverse(add(n,x)) = x + 4 >= x + 4 = app(reverse(x),add(n,nil()))
     
     app(nil(),y) = y >= y = y
     
     app(add(n,x),y) = x + y + 4 >= x + y + 4 = add(n,app(x,y))
    problem:
     DPs:
      
     TRS:
      reverse(nil()) -> nil()
      reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
      app(nil(),y) -> y
      app(add(n,x),y) -> add(n,app(x,y))
    Qed