(string-grobner-system
 "[2*X1-U1,0,0,2*X2-U2,2*X3-U1,2*X4-U2,U2*X6-U1*X5,U1*X6+U2*X5-U1*U2,2*X1*X7-X1^2,2*X2*X8-X2^2,2*X4*X8+2*X3*X7-X4^2-X3^2,2*X6*X8+2*X5*X7-X6^2-X5^2]"
 '(s x1 x2 x3 x4 x5 x6 x7 x8)		;vars
 '(u1 u2)				;parameters
 :cover (list (list "[]" "[u1,u2]"))
 :main-order #'grevlex>
 :parameter-order #'grevlex>
 )