@Carl Love According to ?kernelopts(cpulimit) (I ran it under Maple 2015.1), "The cpulimit, datalimit, and stacklimit limit variables must be used carefully. When a limit is reached Maple may shutdown without warning. The option to save may not be given. On some platforms, including all Windows platforms, the detection of limit violations is tied to garbage collection. Therefore, the detection of limit violations is inaccurate for code that rarely invokes garbage collection. If garbage collection is never invoked, Maple does not detect limit violations."

While the status bar is not mentioned there, maybe this paragraph is relevant to the status bar as well, so maybe the issue that you and @Markiyan Hirnyk disagree on is platform-dependent?

@Carl Love : I guess the point you and @Markiyan Hirnyk disagree on is if the status line update can ONLY be initiated by garbage collection. Your program apparently demonstrates that garbage collection does cause status line update, but I don't think it can demonstrate that there can be no other cause. I don't have my own opinion on the point of the disagreement.

@Mac Dude Thank you for your time and input. Unfortunately, I cannot insert print() into diffalg(04) (http://www-sop.inria.fr/members/Evelyne.Hubert/diffalg/), at least I don't know how. Judging by the maple.ind file there, the distribution is in the internal Maple format .m, which is not user-modifiable (although I may be mistaken). I just use the Rosenfeld_Groebner procedure of that package. Maybe I should approach the author of the package.

@Thomas Richard Thank you, I know that diffalg is deprecated and replaced by DifferentialAlgebra. However, I don't use the standard diffalg from Maple, but its later version diffalg(04) (http://www-sop.inria.fr/members/Evelyne.Hubert/diffalg/), which was not a part of Maple. Actually, I have Maple 2015, but procedure Rosenfeld_Groebner of diffalg(04) does not run with my input under Maple 2015, so I have to use Maple 9. I use diffalg(04) because its version of Rosenfeld_Groebner allows using non-commutative derivations, which is important to me as I am trying to simplify the task using the high symmetry of my problem (it is invariant under the Poincare group) and methods of Hubert, E. Differential Algebra for Derivations with Nontrivial Commutation Rules, Journal of Pure and Applied Algebra (2005), Volume 200, Issues 1-2. (http://www.ens-lyon.fr/LIP/Arenaire/SYMB/teams/cafe/cafe3.pdf) . As far as I know, there is no such functionality in DifferentialAlgebra.

@Mac Dude Thank you for the information. My task is not supposed to produce a lot of output or go into endless loops, although there can be very long loops. Memory swell is a common issue for such problems though. The last value I got was 1.18 GB (yes, gigabyte). This run ended with a "Windows is shutting down" screen for an unknown reason, so I just lost those hours and had to restart the task.

I don't know how long the task is supposed to run, and there is no parameter governing the size of the problem. Unfortunately, this is an "all or nothing" problem. I am trying to perform a differential elimination of some indeterminates from a large overdetermined system of partial differential equations (25 equations) with 18 indeterminates and 4 independent variables. Benchmarks for similar problems can be found at the end of Section 4 of https://arxiv.org/pdf/1108.0817v1.pdf, and the results there vary wildly.