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)))
  TDG 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)))
   graph:
    shuffle#(add(n,x)) -> shuffle#(reverse(x)) ->
    shuffle#(add(n,x)) -> shuffle#(reverse(x))
    shuffle#(add(n,x)) -> shuffle#(reverse(x)) ->
    shuffle#(add(n,x)) -> reverse#(x)
    shuffle#(add(n,x)) -> reverse#(x) ->
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
    shuffle#(add(n,x)) -> reverse#(x) ->
    reverse#(add(n,x)) -> reverse#(x)
    reverse#(add(n,x)) -> reverse#(x) ->
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
    reverse#(add(n,x)) -> reverse#(x) ->
    reverse#(add(n,x)) -> reverse#(x)
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil())) ->
    app#(add(n,x),y) -> app#(x,y)
    app#(add(n,x),y) -> app#(x,y) -> app#(add(n,x),y) -> app#(x,y)
   CDG 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)))
    graph:
     shuffle#(add(n,x)) -> shuffle#(reverse(x)) ->
     shuffle#(add(n,x)) -> reverse#(x)
     shuffle#(add(n,x)) -> shuffle#(reverse(x)) ->
     shuffle#(add(n,x)) -> shuffle#(reverse(x))
     reverse#(add(n,x)) -> app#(reverse(x),add(n,nil())) -> app#(add(n,x),y) -> app#(x,y)
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 3/25
     DPs:
      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)))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [shuffle#](x0) = x0,
       
       [shuffle](x0) = 5x0 + 3,
       
       [reverse](x0) = x0,
       
       [add](x0, x1) = x1 + 1,
       
       [app](x0, x1) = x0 + x1,
       
       [nil] = 0
      orientation:
       shuffle#(add(n,x)) = x + 1 >= x = shuffle#(reverse(x))
       
       app(nil(),y) = y >= y = y
       
       app(add(n,x),y) = x + y + 1 >= x + y + 1 = add(n,app(x,y))
       
       reverse(nil()) = 0 >= 0 = nil()
       
       reverse(add(n,x)) = x + 1 >= x + 1 = app(reverse(x),add(n,nil()))
       
       shuffle(nil()) = 3 >= 0 = nil()
       
       shuffle(add(n,x)) = 5x + 8 >= 5x + 4 = add(n,shuffle(reverse(x)))
      problem:
       DPs:
        
       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)))
      Qed