MAYBE
MAYBE
TRS:
 {
             app(app(app(if(), true()), xs), ys) -> xs,
            app(app(app(if(), false()), xs), ys) -> ys,
                         app(app(sub(), x), 0()) -> x,
       app(app(sub(), app(s(), x)), app(s(), y)) -> app(app(sub(), x), y),
       app(app(gtr(), app(s(), x)), app(s(), y)) -> app(app(gtr(), x), y),
               app(app(gtr(), app(s(), x)), 0()) -> true(),
                         app(app(gtr(), 0()), y) -> false(),
                           app(app(d(), x), 0()) -> true(),
         app(app(d(), app(s(), x)), app(s(), y)) ->
  app(
     app(app(if(), app(app(gtr(), x), y)), false()),
     app(app(d(), app(s(), x)), app(app(sub(), y), x))
  ),
  app(app(filter(), p), app(app(cons(), x), xs)) ->
  app(
     app(app(if(), app(p, x)), app(app(cons(), x), app(app(filter(), p), xs))
     ), app(app(filter(), p), xs)
  ),
                    app(app(filter(), p), nil()) -> nil(),
             app(len(), app(app(cons(), x), xs)) -> app(s(), app(len(), xs)),
                               app(len(), nil()) -> 0()
 }
 DUP: We consider a duplicating system.
  Trs:
   {
               app(app(app(if(), true()), xs), ys) -> xs,
              app(app(app(if(), false()), xs), ys) -> ys,
                           app(app(sub(), x), 0()) -> x,
         app(app(sub(), app(s(), x)), app(s(), y)) -> app(app(sub(), x), y),
         app(app(gtr(), app(s(), x)), app(s(), y)) -> app(app(gtr(), x), y),
                 app(app(gtr(), app(s(), x)), 0()) -> true(),
                           app(app(gtr(), 0()), y) -> false(),
                             app(app(d(), x), 0()) -> true(),
           app(app(d(), app(s(), x)), app(s(), y)) ->
    app(
       app(app(if(), app(app(gtr(), x), y)), false()),
       app(app(d(), app(s(), x)), app(app(sub(), y), x))
    ),
    app(app(filter(), p), app(app(cons(), x), xs)) ->
    app(
       app(
          app(if(), app(p, x)),
          app(app(cons(), x), app(app(filter(), p), xs))
       ), app(app(filter(), p), xs)
    ),
                      app(app(filter(), p), nil()) -> nil(),
               app(len(), app(app(cons(), x), xs)) ->
    app(s(), app(len(), xs)),
                                 app(len(), nil()) -> 0()
   }
  Fail