YES

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)))

linear polynomial interpretations on N:

  app_A(x1,x2) = x1 + x2
  app#_A(x1,x2) = x1 + x2
  nil_A = 0
  nil#_A = 0
  add_A(x1,x2) = x1 + x2 + 1
  add#_A(x1,x2) = x1 + x2 + 1
  reverse_A(x1) = x1
  reverse#_A(x1) = x1
  shuffle_A(x1) = x1 + 1
  shuffle#_A(x1) = x1 + 1

precedence:

  reverse > nil > app = shuffle > add