MAYBE

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))
   ADG 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))
    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))
     shuffle#(add(n,x)) -> reverse#(x) ->
     reverse#(add(n,x)) -> reverse#(x)
     shuffle#(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)) -> reverse#(x) ->
     reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
     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)
    Restore Modifier:
     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)))
     SCC Processor:
      #sccs: 3
      #rules: 3
      #arcs: 8/25
      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)))
      Open
      
      DPs:
       reverse#(add(n,x)) -> 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)))
      Open
      
      DPs:
       app#(add(n,x),y) -> app#(x,y)
      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)))
      Open