Ok, was implementing a heuristic for pair selection. When there is    
   a choice among S-polynomials, I will choose the one with the largest   
   head GCD. The nasty example now runs 3-times faster:   
      
   Old Strategy, Choose oldest S-polynomial:   
      
   ?- X is 5+(5+A^2)*B-A*B^2, Y is 5*A^2*B-(A+4*A^2)*B^2, time(Z is X/Y).   
   % Up 5,352 ms, GC 239 ms, Thread Cpu 5,156 ms (Current 06/25/17 17:28:27)   
   Z is (1+1/4+(1+1/4+1/4*A^2)*B-1/4*A*B^2)/((1+1/4)*A^2*B-(1/4*A+A^2)*B^2)   
      
   New Strategy, Choose S-polynomial with largest head GCD:   
      
   ?- X is 5+(5+A^2)*B-A*B^2, Y is 5*A^2*B-(A+4*A^2)*B^2, time(Z is X/Y).   
   % Up 1,593 ms, GC 164 ms, Thread Cpu 1,422 ms (Current 06/25/17 22:23:01)   
   Z is (1+1/4+(1+1/4+1/4*A^2)*B-1/4*A*B^2)/((1+1/4)*A^2*B-(1/4*A+A^2)*B^2)   
      
   From 5,352 ms to 1,593 ms isn't bad. Not yet as good   
   as the MacSyma result below. But couldn't test the cyclic5   
   and kat5 examples yet, working on.    
      
   Already happy with this improvement!   
      
   Am Sonntag, 11. Juni 2017 04:35:54 UTC+2 schrieb j4n bur53:   
   > I am unable to run derive 6.10 on my windows 10 machine.   
   > On the other hand I could run maxima, which has a groebner   
   > basis library, and I get:   
   >    
   > (%i27)    
   > poly_buchberger([(5+(5+a^2)*b-a*b^2)*t,(5*a^2*b-(a+4*a^2)*b^2)   
   (t-1)],[t,a,b]);   
   > Evaluation took 0.3281 seconds (0.3281 elapsed) using 4.431 MB.   
   > (%o27) [(-a*b^2*t)+a^2*b*t+5*b*t+5*t,   
   >          (-4*a^2*b^2*t)-a*b^2*t+5*a^2*b*t+4*a^2*b^2+a*b^2   
   >                        -5*a^2*b,   
   >          4*a*b^3*t-4*a*b^2*t-20*b^2*t+5*b*t+25*t-4*a^2*b^2   
   >                   -a*b^2+5*a^2*b,   
   >          20*a*b^2*t+5*b^2*t-5*a*b*t+5*b*t-25*a*t-4*a^2*b^3   
   >                    -a*b^3+4*a^3*b^2+6*a^2*b^2-5*a^3*b,   
   >          (-5*b^2*t)+10*a*b*t-105*b*t-25*a^2*t+25*a*t-100*t   
   >                    -4*a^3*b^3+3*a^2*b^3+a*b^3+4*a^4*b^2   
   >                    +2*a^3*b^2+14*a^2*b^2+5*a*b^2-5*a^4*b   
   >                    +5*a^3*b-25*a^2*b,   
   >          (-20*b^3*t)-405*b^2*t+85*a*b*t+115*b*t-75*a*t+500*t   
   >                     +16*a^2*b^4+4*a*b^4-16*a^3*b^3   
   >                     -36*a^2*b^3-3*a*b^3+32*a^3*b^2   
   >                     -62*a^2*b^2-20*a*b^2-15*a^3*b+100*a^2*b,   
   >          4*a^3*b^4+a^2*b^4-4*a^4*b^3-6*a^3*b^3-20*a^2*b^3   
   >                   -5*a*b^3+5*a^4*b^2+5*a^2*b^2-5*a*b^2   
   >                   +25*a^2*b,   
   >          340*b^4*t+7100*b^3*t+2760*b^2*t-9375*b*t-1000*a*t   
   >                   -5375*t-272*a^2*b^5-68*a*b^5+272*a^3*b^4   
   >                   +440*a^2*b^4+8*a*b^4-372*a^3*b^3   
   >                   +1152*a^2*b^3+300*a*b^3+200*a^3*b^2   
   >                   -600*a^2*b^2+215*a*b^2-200*a^3*b   
   >                   -1075*a^2*b,   
   >          20*b^5*t+400*b^4*t-220*b^3*t-975*b^2*t+250*b*t   
   >                  +625*t-16*a^2*b^6-4*a*b^6+16*a^3*b^5   
   >                  +40*a^2*b^5+4*a*b^5-36*a^3*b^4+56*a^2*b^4   
   >                  +20*a*b^4+20*a^3*b^3-120*a^2*b^3-5*a*b^3   
   >                  -75*a^2*b^2-25*a*b^2+125*a^2*b]   
   >    
   > The lcm is the polynomial 4*a^3*b^4 + .... Probably indeed   
   > a nasty example, 0.3281 secs isn´t that fast. Nevertheless   
   > I need to check what heuristic I am missing.   
   >    
   > I also get spoaradic memory overflows for this example,   
   > its a little monster that bugs me.   
   >    
   > P.S.: was using the following maxima loads and flags:   
   >    
   > (%i1) load(grobner);   
   >    
   > (%i21) showtime:true;   
   >    
   > (%i24) display2d:false;   
   >    
   > (%i26) linel:60;   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)