Singular

I have a graded ring and compute syzygies with Singular online (version 4.1.1).
Depending on the order I write the variables I get a different number of syzygies. This looks like a bug.
More precisely:
I generate an ideal with:
ring re = 0, (s,t,w,z(0..3),y(5..7),x(0..2)),wp(1,1,9,15,15,15,15,10,10,10,5,5,5);
ideal parm = w^2-(s^3-t^3)*(s^15+t^15),
z(0)-(s^3-t^3)*w*s^3,z(1)-(s^3-t^3)*w*s^2*t,z(2)-(s^3-t^3)*w*s*t^2,z(3)-(s^3-t^3)*w*t^3,
y(5)-(s^3-t^3)*s^2*t^5,y(6)-(s^3-t^3)*s*t^6,y(7)-(s^3-t^3)*t^7,
x(0)-(s^3-t^3)*s^2,x(1)-(s^3-t^3)*s*t,x(2)-(s^3-t^3)*t^2;
ideal krom= eliminate(parm,w*s*t);
ring r = 0,(z(0..3),y(5..7),x(0..2)),wp(3,3,3,3,2,2,2,1,1,1);
ideal kr = imap(re,krom);
list T = mres(kr,2);
print(betti(T),"betti");

I get 161 syzygies (also not all degrees in the Betti table are OK).
But with
ring r = 0,(x(0..2),y(5..7),z(0..3)),wp(1,1,1,2,2,2,3,3,3,3);
I get 169 syzygies.
But there should only be 160 syzygies.

Can somebody explain me what is happening here?

Best, Jan Stevens

You get a generating set of the syszygy module:
different order of variables may produce a different number of generators.
betti works only for homogeneous input (wrt. weight 1).