Uncomplet flush takes a long time for water to empty in bowl

Water is not draining completely from the toilet line to the sewage tank. If there is a 'low/little slope' section anywhere in that drain line, solids WILL settle and collect there and cause water to back-up in the toilet drain line. Then the toilet will not flush completely or at all until the 'soft blockage' is cleared out and the drain line emptied. Al 'gravity drain' toilets require a free draining/empty drain line that allows flush water to drain unrestricted. A basement toilet has a pump that 'forces' flush water up and out with enough pressure to sometimes force out the 'soft clog.'

Welcome to our new world of water conservation. If you have a toilet that isn't newer....you have something in your trap weir. Or your flapper is malfunctioning. Or your float valve isn't filling your tank correctly. Or your bowl scouring ports could be clogged. There are sooo many things that could cause this....
.New toilets do this because their design to use less water has reached the point of no-longer working to clear the bowl contents. Plain and simple. It has became the norm to flush once for #1's and flush (how ever many it takes to flush all waste) for #2's.
Back to old styles...You can remove the tank top and inspect the water level in the tank(should be about a 1/2" below overflow tube when full), inspect the flapper(flush the toilet and see if your flapper is staying up long enough to allow enough water to enter the bowl to cause a syphon action that ends with a suction sound and complete emptying of the water from the bowl), flush your toilet and look in the bowl to see if the water spraying from your rim is adequately dispensing water to scour the sides of the bowl, and also look at the jet that shoots water from the bottom of the bowl...aimed toward the outlet portion of the very bottom of the interior bowl. This jet is what starts the syphon action that empties your bowl. If you have something stuck in your trap weir....you probably need to call your Plumber to auger the object out or break it down to a size that will pass into the sewer.
The small ports that spray your sides can be cleared with a 3/16" stiff nylon brush...the jet down below can be cleared with a 1" stiff nylon brush. Flapper malfunction is repaired by replacing the flapper. Incorrect water level in the tank can be fixed by adjusting the valve float. but chances are that if it is all of a sudden malfunctioning...it probably needs to be replaced...good luck and always know how to turn your water off before starting work on your plumbing.
Be gentle with the parts inside your toilet tank. Using a calcium remover when clearing bowl inner ports and jets will help tremendously....but be certain to read the container and follow all handling/use instructions you read. Be careful.....Nick

I have the same problem with my Toto TS703. When you flush it, it fills the bowl with water to the rim and stops. Within an hour, the water in the bowl is totally empty except for a small puddle. This has been going on for a few days. It was installed 3 years ago and never had a problem with it until now.

You are describing a couple of possible problems, neither of which have super easy solutions.
The worst case senario is that there is a crack in the passageway the water travels when it is flushed and just happens to be at a spot that allows the leaky water to go into the floor drain and not on the floor. This is most likely to happen in a brand new toilet situation in which case you take the bowl back to where it was purchased and exchange it.

The most likely scenario however is that there is some form of material caught in the passageway and is "wicking" the water out of the bowl. As water in the bowl disappears from view when you flush, it travels uphill for a moment....over a hump..and then down to continue its journey to the sewer drain. When a piece of material is caught laying over that hump with one end in the bowl water and the other end hanging in empty space, it will draw the water out of the bowl "wick" just like a wick in an oil lamp sucks the oil up through it so the flame continues to burn the oil and not the wick.
Often times just using a plunger vigorously, after a flush and the bowl has refilled, for a couple of minutes will help get the pesky piece over the hump. Otherwise only a special toilet snake (most often called a closet auger) will solve this issue. If you need to get this auger, Do NOT think if it costs more then it must be better. They can range up to $35 or more. You should be able to get this tool, that hopefully you will never have to use again, for between $10 to $15

If bowl is emptying, the most common cause is a crack in the bowl. I have however seen a string get hung in the throat and siphon the water out slowly. May want to pull stool and take a good look. Hope this helps.

The flapper isn't staying open long enought, try holding down the handel for a few seconds each time u flush.

Sounds like your toilet is not vented properly. Possilbly something caught in the trap is causing it to syphon

it sounds like it is not flushing completely at first and then releases and the suction is pulling water out of the bowl. Could be a venting issue or a clog issue that is hindering the proper flushing of the toilet.

make sure water level is sat at factory settings. there should be a black line that reads WATER LEVEL. If this is not the problem. then you have calci buildup. get a gal. of muratic acid,plunge all water out of toilet bowl. then dump in at least 1/2 gal. let set over nite. with water turned off. get up turn on water then flush. You mite have to do it twrice. hope this helps you.... duane.