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Questions about handling with inequalities with, e.g., Reduce, Solve, FindInstance etc., their application in defining Regions, and ways to incorporate them into other computations, e.g. integration.

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. I will repost an improved version of the question in the future. I have a set of inequalities in $$x_0,x_2,x_3,x_4$$ Each inequality is of the form $$\max \{T_1,T_2,\dots\}<c$$ where each $T_i … minutes after starting Mathematica). Questions: How can I get rid of the opening and closing "Abort Dynamic Evaluation" windows? How can I find a solution for my system of inequalities? PS …
asked Aug 2 by user66834