EVAL> (STRING-GROBNER-SYSTEM
          "[a-l3*c1*c2+l3*s1*s2-l2*c1, b-l3*c1*s2-l3*c2*s1-l2*s1, c1^2+s1^2-1, c2^2+s2^2-1]"
          '(C2 S2 C1 S1) '(A B L2 L3) :COVER '(("[]" "[l2,l3]")))
Condition:
  Green list: [  ]
  Red list: [ L3, A^2 + B^2, L2, A ]
 Basis: [ ( - 2 * A * L2) * C1 + ( - 2 * B * L2) * S1 + (A^2 + B^2 + L2^2 - L3^2), (4 * A^2 * L2^2 + 4 * B^2 * L2^2) * S1^2 + ( - 4 * A^2 * B * L2 - 4 * B^3 * L2 - 4 * B * L2^3 + 4 * B * L2 * L3^2) * S1 + (A^4 + 2 * A^2 * B^2 - 2 * A^2 * L2^2 - 2 * A^2 * L3^2 + B^4 + 2 * B^2 * L2^2 - 2 * B^2 * L3^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4), ( - 2 * A * L2 * L3) * S2 + ( - 2 * A^2 * L2 - 2 * B^2 * L2) * S1 + (A^2 * B + B^3 + B * L2^2 - B * L3^2), ( - 2 * L2 * L3) * C2 + (A^2 + B^2 - L2^2 - L3^2) ]
Condition:
  Green list: [ A^2 + B^2 ]
  Red list: [ L3, B * L2^2 - B * L3^2, L2, A ]
 Basis: [ ( - 4 * B * L2^3 + 4 * B * L2 * L3^2) * S1 + (4 * B^2 * L2^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4), (4 * A * B * L2^3 * L3 - 4 * A * B * L2 * L3^3) * S2 + ( - 2 * B^2 * L2^4 + 4 * B^2 * L2^2 * L3^2 - 2 * B^2 * L3^4), ( - 2 * L2 * L3) * C2 + ( - L2^2 - L3^2), (4 * A * L2^3 - 4 * A * L2 * L3^2) * C1 + (4 * B^2 * L2^2 - L2^4 + 2 * L2^2 * L3^2 - L3^4) ]
Condition:
  Green list: [ A^2 + B^2, L2^2 - L3^2 ]
  Red list: [ B^2, L3, A, L2 ]
 Basis: [ (4 * B^2 * L3^2) ]
Condition:
  Green list: [ A ]
  Red list: [ L3, B, L2 ]
 Basis: [ ( - 2 * B * L2) * S1 + (B^2 + L2^2 - L3^2), ( - 2 * L2 * L3) * C2 + (B^2 - L2^2 - L3^2) ]
Condition:
  Green list: [ A, B ]
  Red list: [ L3, L2, L2^2 - L3^2 ]
 Basis: [ (L2^2 - L3^2) ]
Condition:
  Green list: [ A, B, L2^2 - L3^2 ]
  Red list: [ L3, L2 ]
 Basis: [ ]
real time : 10.183 secs
run time  : 9.017 secs
VALUES--> NIL