@Alejandro Jakubi 

I've given you the 'full code' except for the exact declarations of the expressions (which are very normal). So, I'm afraid it is a problem in the pacakge DifferentialAlgebra.

So, it seems this problem cannot be solved directly. Wel, that's an answer too for me.

Many thanks!

@Alejandro Jakubi 


Concerning the javaheaplimit. I'm not using any visualisation (such as a plot) so I suppose the javaheaplimit is not really restrictive here..

I'm sorry, but I neglected to to write the full error-message, i.e.,
          Error, (in DifferentialAlgebra:-RosenfeldGroebner) out of memory error

I've should have put this in my original question. So, yes, it is most likely related to the package DifferentialAlgebra.

I'm not  throwing the full code on-line since it applies to some research I've been doing, not yet published and all..I'll give an outline of the code with some outputs

>> restart:
>> with(StringTools):FormatTime(); # to get a time-stamp of the last execution of the code
>>  a:= kernelopts('bytesalloc');
                                          8781824
      kernelopts('datalimit');
                                          infinity    
      kernelopts(jvmheaplimit = 1000*1000*Unit('kibibyte'));
                                          1000000
      a:= kernelopts('stacklimit'):
      kernelopts(stacklimit = 2*a*Unit('kibibyte')):
     kernelopts('stacklimit');
                                            16320
      a:= kernelopts('cacheclearlimit'):
      kernelopts(cacheclearlimit = 1000000*a*Unit('kibibyte')):
      kernelopts('cacheclearlimit');
                                             524288000000
                         
>> with(DifferentialAlgebra):      with(Tools):
>> #Introduction of Round procedure
      Round := proc (x, n::integer := 1) `~`[parse](`~`[sprintf](cat("%.", n, "f"), x)) end proc: # i use this to round some floats
>> DECLARATION of expressions equal to an integer or rational number
     For example:

     V:=300;
                                       V:=300
     P := 1013/100:
                                       P := 1013/100:

>> Declaration of expression equal to a relation of variables
     For example:
    
     s1    :=  -x1[t]  + k1  * x1 * x2 * x3 * x4
                                                
                                   s1    :=  -x1_t + k1 x1 x2 x3 x4
    
     eq1 := s1 * V;
                                    eq1 := - 300 x1_t + 300 k1 x1 x2 x3 x4
     eq2 := v1-x1;
                                   t1 := v1 - x1

>> # Declaration of a differential ring:
 Definition of differential ring ##############
ring := DifferentialAlgebra:-DifferentialRing(blocks = [[x1(t), x2(t), etc.],[v1(t), v2(t), etc.]], derivations = [t],arbitrary = [k1(),k2(),k3(), etc. ]);
                                                        

                                     ring := differential_ring

simplified_sys := RosenfeldGroebner([eq1, eq2, etc.],ring,singsol=none);
      Error, (in DifferentialAlgebra:-RosenfeldGroebner) out of memory error