To each vertex of a regular pentagon an integer is assigned, so that the sum of all five numbers is positive. If three consecutive vertices are assigned the numbers
![x,y,z](/media/m/b/7/2/b72c022e9d438802d328d34eb61bb4ba.png)
respectively, and
![y<0](/media/m/a/d/4/ad4d95d8241ceabd8db9cb0dfa2e85c4.png)
, then the following operation is allowed:
![x,y,z](/media/m/b/7/2/b72c022e9d438802d328d34eb61bb4ba.png)
are replaced by
![x+y,-y,z+y](/media/m/9/2/e/92e3518b0367387db91d3d4ae688dbbb.png)
respectively. Such an operation is performed repeatedly as long as at least one of the five numbers is negative. Determine whether this procedure necessarily comes to an end after a finite number of steps.
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To each vertex of a regular pentagon an integer is assigned, so that the sum of all five numbers is positive. If three consecutive vertices are assigned the numbers $x,y,z$ respectively, and $y<0$, then the following operation is allowed: $x,y,z$ are replaced by $x+y,-y,z+y$ respectively. Such an operation is performed repeatedly as long as at least one of the five numbers is negative. Determine whether this procedure necessarily comes to an end after a finite number of steps.