A small ideal hard to factorize

This ideal has a primary decomp with 8 factors (7 prime), found via tricks.
One prime factor is complicated, but the rest are really quite simple.
You may find this an interesting challenge. Details provided if requested

Greetings,
Peter Johnson
Recife, Brazil

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ring rr = 0,(o,K,L,M,N,P,Q,R,S,T,U,V,W),dp;

ideal ts; /* 5, Gr base 16 */
ts[1]=MR-MU+NV-QV;
ts[2]=oMU-oNV+MP-PV;
ts[3]=oNR-oQU+NP-PQ+PR-PU;
ts[4]=oKPR-oNPT+oQ2U-oQRU+KP2-NPQ+PQ2-PQR+PR2-NPS+PRS-P2T+PQU-PRU;
ts[5]=oLPQ-oNQU+oQU2-oPUW+LP2+PQS-NPU+PQU-PSU-P2W;

My colleague Sebastian Jambor tested this example with the last version of MAGMA. He stopped it after half an hour.

Mohamed