MAYBE
MAYBE
TRS:
 {
   app(app(app(app(filter2(), true()), f), x), xs) ->
  app(app(cons(), x), app(app(filter(), f), xs)),
  app(app(app(app(filter2(), false()), f), x), xs) ->
  app(app(filter(), f), xs),
                 app(app(app(if(), true()), x), y) -> x,
                app(app(app(if(), false()), x), y) -> y,
          app(app(le(), app(s(), x)), app(s(), y)) -> app(app(le(), x), y),
                  app(app(le(), app(s(), x)), 0()) -> false(),
                            app(app(le(), 0()), y) -> true(),
          app(app(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                  app(app(eq(), app(s(), x)), 0()) -> false(),
                  app(app(eq(), 0()), app(s(), y)) -> false(),
                          app(app(eq(), 0()), 0()) -> true(),
        app(app(min(), x), app(app(cons(), y), z)) ->
  app(
     app(app(if(), app(app(le(), x), y)), app(app(min(), x), z)),
     app(app(min(), y), z)
  ),
                         app(app(min(), x), nil()) -> x,
        app(app(del(), x), app(app(cons(), y), z)) ->
  app(
     app(app(if(), app(app(eq(), x), y)), z),
     app(app(cons(), y), app(app(del(), x), z))
  ),
                         app(app(del(), x), nil()) -> nil(),
       app(app(map(), f), app(app(cons(), x), xs)) ->
  app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                         app(app(map(), f), nil()) -> nil(),
    app(app(filter(), f), app(app(cons(), x), xs)) ->
  app(app(app(app(filter2(), app(f, x)), f), x), xs),
                      app(app(filter(), f), nil()) -> nil(),
            app(minsort(), app(app(cons(), x), y)) ->
  app(
     app(cons(), app(app(min(), x), y)),
     app(
        minsort(),
        app(app(del(), app(app(min(), x), y)), app(app(cons(), x), y))
     )
  ),
                             app(minsort(), nil()) -> nil()
 }
 DUP: We consider a duplicating system.
  Trs:
   {
     app(app(app(app(filter2(), true()), f), x), xs) ->
    app(app(cons(), x), app(app(filter(), f), xs)),
    app(app(app(app(filter2(), false()), f), x), xs) ->
    app(app(filter(), f), xs),
                   app(app(app(if(), true()), x), y) -> x,
                  app(app(app(if(), false()), x), y) -> y,
            app(app(le(), app(s(), x)), app(s(), y)) -> app(app(le(), x), y),
                    app(app(le(), app(s(), x)), 0()) -> false(),
                              app(app(le(), 0()), y) -> true(),
            app(app(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                    app(app(eq(), app(s(), x)), 0()) -> false(),
                    app(app(eq(), 0()), app(s(), y)) -> false(),
                            app(app(eq(), 0()), 0()) -> true(),
          app(app(min(), x), app(app(cons(), y), z)) ->
    app(
       app(app(if(), app(app(le(), x), y)), app(app(min(), x), z)),
       app(app(min(), y), z)
    ),
                           app(app(min(), x), nil()) -> x,
          app(app(del(), x), app(app(cons(), y), z)) ->
    app(
       app(app(if(), app(app(eq(), x), y)), z),
       app(app(cons(), y), app(app(del(), x), z))
    ),
                           app(app(del(), x), nil()) -> nil(),
         app(app(map(), f), app(app(cons(), x), xs)) ->
    app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                           app(app(map(), f), nil()) -> nil(),
      app(app(filter(), f), app(app(cons(), x), xs)) ->
    app(app(app(app(filter2(), app(f, x)), f), x), xs),
                        app(app(filter(), f), nil()) -> nil(),
              app(minsort(), app(app(cons(), x), y)) ->
    app(
       app(cons(), app(app(min(), x), y)),
       app(
          minsort(),
          app(app(del(), app(app(min(), x), y)), app(app(cons(), x), y))
       )
    ),
                               app(minsort(), nil()) -> nil()
   }
  Fail