MAYBE MAYBE TRS: { app(app(append(), app(app(append(), l1), l2)), l3) -> app(app(append(), l1), app(app(append(), l2), l3)), app(app(append(), app(app(cons(), h), t)), l) -> app(app(cons(), h), app(app(append(), t), l)), app(app(append(), nil()), l) -> l, app(app(map(), f), app(app(append(), l1), l2)) -> app(app(append(), app(app(map(), f), l1)), app(app(map(), f), l2)), app(app(map(), f), app(app(cons(), h), t)) -> app(app(cons(), app(f, h)), app(app(map(), f), t)), app(app(map(), f), nil()) -> nil() } DUP: We consider a duplicating system. Trs: { app(app(append(), app(app(append(), l1), l2)), l3) -> app(app(append(), l1), app(app(append(), l2), l3)), app(app(append(), app(app(cons(), h), t)), l) -> app(app(cons(), h), app(app(append(), t), l)), app(app(append(), nil()), l) -> l, app(app(map(), f), app(app(append(), l1), l2)) -> app(app(append(), app(app(map(), f), l1)), app(app(map(), f), l2)), app(app(map(), f), app(app(cons(), h), t)) -> app(app(cons(), app(f, h)), app(app(map(), f), t)), app(app(map(), f), nil()) -> nil() } Fail