This reflection discusses the s similar example as discussed in: 2.1 Example 1: The twin "paradox".
In order to explain the difference between "proper time" and "coordinate time" we study two experiments:
1) First a "real" experiment and 2) a thought experiment.
In the real experiment we try as good as possible to actual perform the same experiment as depicted in paragraph 2.1.
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The picture at the left shows two observers.
 Observer 1 stays at home. He starts his clock and waits. On his clock he observes the ticks of his clock 1,2,3,4,5,6,7 and 8. These ticks are depicted in the line AB.
 Observer 2 also starts his clock and at the same time he moves away as fast as he can in a certain direction.
He observes the ticks 1,2 and then he stops and travel backs as fast he can. His clocks ticks 3 and 4 and he is back at base.
 Immediate they compare clock readings. Observer 1 his clock shows 8 ticks and clock 2 shows 4 ticks. That means observers 2 his clock runs behind. This is the same result as in paragraph 2.1 An identical result would be 1000 ticks versus 500 ticks.
 The result 1000 versus 990 means that the speed of observer 2 is much slower.

Now we are going to do a thought experiment to simulate this experiment. Observer 1 and 2 are sitting near each other.
 Both say start and the experiment starts. Observer 2 starts his enigine and moves away
 After a certain time Observer 2 says: My clock reads 1. Immediate observer 1 says: My clock reads 2.
 After the same interval observer 2 says: My clock reads 2. Immediate observer 1 says: My clock reads 4.
 After the same interval observer 2 says: My clock reads 3. Immediate observer 1 says: My clock reads 6.
 After the same interval observer 2 says: My clock reads 4. Immediate observer 1 says: My clock reads 8.
What Observer 1 does, because he knows the final outcome, whenever Observer 2 shows a clock reading he multiplies
this number with 2 such that when the two meet again there clock readings agree.
What you can learn from this experiment that the moving clock runs slower than the clock at rest. You can also say this different that the clock which travels the longest path runs the slowest.
Related to the concepts "proper time" versus "coordinate time" this means that the clock at rest shows coordinate time and the moving clock shows "proper time".
The question is is that always the case.
To challenge that we are first performing a thought experiment. However slightly different.
Observer 1 and 2 agree that before the experiment start they both will start there engines. They also agree that Observer 2 will not return when his clock reading is 2 ticks.
 Both say start and the experiment starts. Observer 1 will immediate stop his engine (speed). Observer 1 will move away from Observer 2
 After a certain time Observer 2 says: My clock reads 1. Immediate observer 1 says: My clock reads 2.
 After the same interval observer 2 says: My clock reads 2. Immediate observer 1 says: My clock reads 4.
At that same moment Observer 1 will start his engine in turbo speed (much faster than Observer 2) in the direction
of Observer 2.
 After the same interval observer 2 says: My clock reads 3. Immediate observer 1 says: My clock reads 5. And they meet each other. (observer 1 reduces his speed)
What this thought experiment demonstrates is that Observer 2 is now the observer at rest and Observer 1 is the moving observer which travels a certain path relatif to observer 2. However the clock of Observer 1 runs the fastest and his path travelled is the longest compared to observer 2 which stayed at rest. This is in conflict with the first experiment where the path of observer 2 was the longest and his clock runs the lowest.
What this shows that when you consider yourself at rest it is possible that you can perform experiments which demonstrates that your clock runs the fastest and moving clocks slower, but there is no garantee that this is always the case. It is possible that there are moving clocks (relatif to you), which run faster.