MAYBE MAYBE TRS: { app(app(app(app(insert(), f), g), nil()), y) -> app(app(cons(), y), nil()), app(app(app(app(insert(), f), g), app(app(cons(), x), z)), y) -> app( app(cons(), app(app(f, x), y)), app(app(app(app(insert(), f), g), z), app(app(g, x), y)) ), app(app(app(sort(), f), g), nil()) -> nil(), app(app(app(sort(), f), g), app(app(cons(), x), y)) -> app(app(app(app(insert(), f), g), app(app(app(sort(), f), g), y)), x), app(app(max(), x), 0()) -> x, app(app(max(), app(s(), x)), app(s(), y)) -> app(app(max(), x), y), app(app(max(), 0()), y) -> y, app(app(min(), x), 0()) -> 0(), app(app(min(), app(s(), x)), app(s(), y)) -> app(app(min(), x), y), app(app(min(), 0()), y) -> 0(), app(asort(), z) -> app(app(app(sort(), min()), max()), z), app(dsort(), z) -> app(app(app(sort(), max()), min()), z) } DUP: We consider a duplicating system. Trs: { app(app(app(app(insert(), f), g), nil()), y) -> app(app(cons(), y), nil()), app(app(app(app(insert(), f), g), app(app(cons(), x), z)), y) -> app( app(cons(), app(app(f, x), y)), app(app(app(app(insert(), f), g), z), app(app(g, x), y)) ), app(app(app(sort(), f), g), nil()) -> nil(), app(app(app(sort(), f), g), app(app(cons(), x), y)) -> app(app(app(app(insert(), f), g), app(app(app(sort(), f), g), y)), x), app(app(max(), x), 0()) -> x, app(app(max(), app(s(), x)), app(s(), y)) -> app(app(max(), x), y), app(app(max(), 0()), y) -> y, app(app(min(), x), 0()) -> 0(), app(app(min(), app(s(), x)), app(s(), y)) -> app(app(min(), x), y), app(app(min(), 0()), y) -> 0(), app(asort(), z) -> app(app(app(sort(), min()), max()), z), app(dsort(), z) -> app(app(app(sort(), max()), min()), z) } Fail