We have a finite, non-strict order on expressions:
$$a+b+c+d > a+b+c = a+b+d > a+b > \dots$$
Every expression is a sum of a set of variables, there are no constants.
If there is a real solution to the system, can we claim that there is a rational one?
For example, in the picture there is a possible rational solution to the system which represents the paths: $$a+b > a+c > a > b+c > b > a$$ Can we construct a network with rational distances given a network with real distances?
Thanks!