I am trying to find example of two bounded monotone sequences, one increasing and one decreasing, such that the product is not a monotone sequence. 

I have tried many of examples, but all my products are monotone. It makes me wonder if the boundedness somehow makes the sequences end up always monotone? Of course, it is easy to find non-bounded monotone functions such that the product is not monotone.

Thanks for the help, sorry if bad English.