I am trying to solve a system of nonlinear equations symbolically using Solve. The input runs for only ~30 seconds, then my syntax highlighting goes black, and there is no output (see below):

Does this mean my kernel has crashed? Mathematica uses almost no RAM as this runs, and just to be sure, I have now constrained the memory so my code is

MemoryConstrained[
 Solve[a1*rtn + a2*rtc + a3*in + a4*ic + a5*rdc + a6 == 0 &&
   a7*rtn + a8*rtc + a9*in + a10*ic + a11*ic*rtc + a12*in*rtn + a13 == 0 &&
   a14*in + a15*ic + a16*in*rtn + a17 == 0 &&
   a18*rtn + a19*rtc + a20*ic + a21*in + a22*rdc + a23*in*rtn + a24 == 0 &&
   a25*in + a26*ic + a27*in*rtn + a28*ic*rtc + a29 == 0, {rtn, rtc, rdc, in, ic}], 10^8]

which also does the same thing. I have also tried to run this on a separate machine, and it also crashes with no output. Both the machines are Linux.