PASS (F) k = 1 off the line: dim S_1Q = 9, D_3' = C[Y,Z]_4 + C X^4  [0.2s]
PASS (K) L0_0: a triple of local length 38 (stable N = 9) <= 38  [17.4s]
     triple: [-2*x^5 - 3*x^4*y + 4*x^3*y^2 + 4*x^2*y^3 + 5*x*y^4 + 5*y^5 - 3*x^4*z + 2*x^3*y*z - 4*x^2*y^2*z + 4*x*y^3*z - 3*y^4*z + 3*x^3*z^2 - 2*x^2*y*z^2 + 2*x*y^2*z^2 - 2*y^3*z^2 + x^2*z^3 - 3*y^2*z^3 + 4*x*z^4 + 4*y*z^4 - 3*z^5 + 2*x^3*y - 4*x^2*y^2 + x*y^3 - y^4 - 2*x^3*z + x^2*y*z - 8*x*y^2*z - 2*y^3*z + x^2*z^2 - 3*x*y*z^2 + 3*y^2*z^2 + 3*x*z^3 - 4*y*z^3 + 5*z^4 - x^2*y - 2*x*y^2 - 3*x^2*z - 2*x*y*z - 2*x*z^2, 5*x^5 + 2*x^4*y + 5*x^3*y^2 - x^2*y^3 - 5*x*y^4 - y^5 - 4*x^3*y*z + 5*x^2*y^2*z - x*y^3*z + y^4*z + x^3*z^2 + 3*x^2*y*z^2 - 4*x*y^2*z^2 + 3*y^3*z^2 + 5*x^2*z^3 + 4*x*y*z^3 - 5*y^2*z^3 + 5*x*z^4 - 5*y*z^4 + 3*z^5 + 3*x^3*y - 2*x^2*y^2 - 2*x*y^3 - 5*y^4 + 4*x^3*z - x^2*y*z + 4*x*y^2*z - y^3*z + x^2*z^2 - x*y*z^2 - 4*y^2*z^2 + 3*x*z^3 + 3*y*z^3 - 5*z^4 + x^2*y + 2*x*y^2 + x^2*z + 4*x*y*z - 2*x*z^2, x^5 + 4*x^4*y - 4*x^3*y^2 + 4*x^2*y^3 + x*y^4 - 3*y^5 - 2*x^4*z - 3*x^3*y*z - x*y^3*z + 4*y^4*z + 2*x^3*z^2 + x^2*y*z^2 - x*y^2*z^2 - 4*y^3*z^2 - 4*x^2*z^3 - 5*x*y*z^3 - y^2*z^3 + 4*x*z^4 + 5*y*z^4 + 3*z^5 - 4*x^3*y - 2*x^2*y^2 + 4*x*y^3 + 2*y^4 - 4*x^3*z - 5*x*y^2*z - y^3*z - 9*x^2*z^2 + 3*y^2*z^2 + x*z^3 - 3*y*z^3 - 3*z^4 - 5*x^2*y - 5*x*y^2 + 3*x^2*z + 3*x*y*z + 3*x*z^2]
PASS (K) L0_1: a triple of local length 39 (stable N = 10) <= 39  [49.8s]
     triple: [-3*x^5 + 3*x^4*y + x^3*y^2 - 5*x^2*y^3 + 2*x^4*z - 4*x^3*y*z - 5*x^2*y^2*z - 2*x*y^3*z - y^4*z - x^3*z^2 - 4*x^2*y*z^2 - x*y^2*z^2 - 4*y^3*z^2 - x^2*z^3 - 4*x*y*z^3 - 5*y^2*z^3 - 5*x*z^4 + 4*y*z^4 - 3*z^5 + 3*x^3*y + x^2*y^2 - 5*x*y^3 - x^3*z + x^2*y*z + 4*x*y^2*z + 2*y^3*z + 5*x^2*z^2 - 6*x*y*z^2 + 5*y^2*z^2 - 2*x*z^3 + 5*y*z^3 - 5*x^2*y + 5*x*y^2 + 4*x^2*z + 5*x*z^2, x^5 - 4*x^4*y + x^3*y^2 - 2*x^2*y^3 + x*y^4 - y^5 - 3*x^4*z + 2*x^3*y*z - 3*x^2*y^2*z - 3*x*y^3*z - 4*y^4*z + 2*x^3*z^2 - 3*x^2*y*z^2 - 3*x*y^2*z^2 - y^3*z^2 + 3*x*y*z^3 + 3*y^2*z^3 + x*z^4 - 4*y*z^4 - 3*z^5 - 5*x^2*y^2 + 3*x*y^3 + x^3*z + 10*x^2*y*z + 2*x*y^2*z - 3*y^3*z + 5*x^2*z^2 - 2*x*y*z^2 - 3*y^2*z^2 + x*z^3 + 2*y*z^3 - z^4 + x^2*y + x*y^2 + 2*x^2*z - 4*x*y*z - 5*x*z^2, x^5 - 3*x^3*y^2 - 2*x^2*y^3 + 4*x*y^4 + 4*y^5 - 5*x^4*z + 4*x^3*y*z - x^2*y^2*z - x*y^3*z - x^3*z^2 - 4*x^2*y*z^2 + 5*y^3*z^2 - x^2*z^3 + 4*x*y*z^3 + y^2*z^3 - 2*x*z^4 + 4*y*z^4 - 5*z^5 + 4*x^3*y - 3*x^2*y^2 + 4*x*y^3 - 5*x^3*z + 5*x^2*y*z - 3*x*y^2*z - 2*y^3*z + 2*x^2*z^2 - 2*x*y*z^2 + 4*y^2*z^2 - 3*x*z^3 + 2*z^4 - 4*x^2*y - x*y^2 + 3*x^2*z]
PASS (K) L0_2: a triple of local length 40 (stable N = 10) <= 40  [90.1s]
     triple: [3*x^5 - x^4*y - 2*x^3*y^2 - 3*x^2*y^3 + 3*x*y^4 - y^5 + 3*x^4*z - x^3*y*z - 3*x^2*y^2*z - 3*x*y^3*z - 2*y^4*z - 3*x^3*z^2 + x^2*y*z^2 - 4*x*y^2*z^2 + 2*y^3*z^2 + 4*x*y*z^3 + 2*y^2*z^3 + x*z^4 - 4*y*z^4 + 5*z^5 + 3*x^3*y - 7*x^2*y^2 - 2*x*y^3 - 2*x^3*z - x^2*y*z + 3*x*y^2*z - 6*x*y*z^2 + 3*y^2*z^2 - 5*x*z^3 + y*z^3 - 5*z^4 + x^2*y - x^2*z + x*y*z + x*z^2, 5*x^5 + 4*x^3*y^2 + 3*x^2*y^3 - 2*x*y^4 + 4*y^5 - 4*x^4*z + 2*x^2*y^2*z + 4*x*y^3*z - 5*y^4*z + 5*x^3*z^2 + x^2*y*z^2 + x*y^2*z^2 + 3*y^3*z^2 + 4*x^2*z^3 - 4*x*y*z^3 + 4*y^2*z^3 + 2*x*z^4 + 2*y*z^4 + 2*z^5 + x^3*y - 6*x^2*y^2 - 3*x*y^3 - 4*x^3*z - 5*x^2*y*z + 6*x*y^2*z - 5*x^2*z^2 + x*y*z^2 - 4*y^2*z^2 - 4*x*z^3 + 2*x*y^2 - x*y*z - 4*x*z^2, x^5 + x^3*y^2 + x^2*y^3 + 3*x*y^4 + 2*y^5 + 5*x^4*z - 2*x^3*y*z + 2*x^2*y^2*z - 5*x*y^3*z - y^4*z + 3*x^3*z^2 + 2*x^2*y*z^2 - x*y^2*z^2 - 2*y^3*z^2 - 5*x^2*z^3 - 5*x*y*z^3 + y^2*z^3 + 5*x*z^4 + 3*y*z^4 - 5*z^5 - 2*x^3*y - 3*x^2*y^2 + 5*x*y^3 - x^3*z + 10*x^2*y*z + 7*x*y^2*z + 2*x^2*z^2 + y^2*z^2 - 4*x*z^3 - y*z^3 - 3*z^4 + 5*x^2*y + 3*x*y^2 - x^2*z - x*y*z - 3*x*z^2]
PASS (K) L0_3: a triple of local length 41 (stable N = 10) <= 41  [118.6s]
     triple: [-x^5 + 3*x^4*y + x^3*y^2 + 5*x^2*y^3 + 3*x*y^4 + 4*y^5 + 2*x^4*z - 4*x^3*y*z + 4*x^2*y^2*z + 2*x*y^3*z + 3*y^4*z - 3*x^3*z^2 + 3*x^2*y*z^2 - 2*x*y^2*z^2 + 4*y^3*z^2 - x^2*z^3 + 5*x*y*z^3 - 4*x*z^4 - 5*y*z^4 - 2*z^5 + 5*x^3*y + x^2*y^2 + 4*x*y^3 - x^3*z - 3*x^2*y*z - 2*x*y^2*z + 4*x^2*z^2 - 2*x*y*z^2 - 2*x*z^3 - 2*y*z^3 + 2*z^4 - 4*x^2*y + x*y^2 - 5*x^2*z + x*y*z - 3*x*z^2, 5*x^5 - 5*x^4*y - 5*x^3*y^2 + 4*x^2*y^3 + x*y^4 + 4*y^5 - 2*x^4*z + 3*x^3*y*z + x^2*y^2*z - 3*x*y^3*z + 4*y^4*z - 3*x^3*z^2 - 4*x^2*y*z^2 - x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 + 4*y^2*z^3 - 2*x*z^4 + 4*y*z^4 - z^5 - 2*x^3*y - 3*x^2*y^2 + x*y^3 - x^3*z + 3*x^2*y*z - 3*x*y^2*z - 5*x^2*z^2 + 5*x*y*z^2 - 3*x*z^3 - 2*y*z^3 - 2*z^4 - x^2*y + 3*x*y^2 + 4*x^2*z - 5*x*y*z + 4*x*z^2, 4*x^5 + 4*x^4*y - 5*x^3*y^2 - 3*x^2*y^3 - 2*x*y^4 - y^5 + x^4*z - 4*x^3*y*z - 3*x^2*y^2*z - 2*x*y^3*z - 3*x^3*z^2 - 2*x^2*y*z^2 + 4*x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 + 4*x*y*z^3 - y^2*z^3 - 5*y*z^4 - 2*z^5 + 5*x^3*y + 4*x*y^3 - 4*x^3*z - 3*x*y^2*z - 4*x^2*z^2 + 3*x*y*z^2 - 3*x*z^3 + y*z^3 - 2*z^4 + 2*x*y^2 + x^2*z + x*y*z - 4*x*z^2]
PASS (K) L0_0 + (x^4): a triple of local length 37 (stable N = 9) <= 37  [139.4s]
     triple: [-4*x^5 + x^4*y - 2*x^3*y^2 - 2*x*y^4 + 2*y^5 - 5*x^4*z - 4*x^3*y*z - 3*x^2*y^2*z - 5*x*y^3*z - 2*y^4*z + 2*x^3*z^2 - 4*x^2*y*z^2 - 2*x*y^2*z^2 + 4*y^3*z^2 + 4*x^2*z^3 + 2*x*y*z^3 + 3*x*z^4 - 5*y*z^4 - 3*z^5 - 5*x^4 - x^3*y - 4*x^2*y^2 + 3*x*y^3 + y^4 + 4*x*y^2*z - 4*y^3*z + 5*x^2*z^2 + 10*x*y*z^2 - 3*y^2*z^2 + x*z^3 + 5*y*z^3 - 2*z^4 + 2*x^2*y - 5*x*y^2 + 3*x^2*z - 2*x*y*z - x*z^2, 3*x^5 - 5*x^4*y - x^3*y^2 - 2*x^2*y^3 - x*y^4 - 4*y^5 - x^4*z - x^3*y*z + 2*x^2*y^2*z - 2*x*y^3*z - y^4*z - 2*x^3*z^2 + x^2*y*z^2 - 4*x*y^2*z^2 + 4*y^3*z^2 + 2*x^2*z^3 + 5*x*y*z^3 + 5*y^2*z^3 + 5*x*z^4 - 2*z^5 - 3*x^4 - 2*x^3*y + 5*x^2*y^2 + x*y^3 - 5*y^4 - 5*x^3*z + 5*x^2*y*z - 8*x*y^2*z - 3*y^3*z - 4*x^2*z^2 + 4*x*y*z^2 + 3*y^2*z^2 + 3*x*z^3 - 5*z^4 + 5*x^2*y + 3*x^2*z - 4*x*y*z - 2*x*z^2, -5*x^5 + 3*x^4*y + 3*x^3*y^2 + 2*x^2*y^3 + 3*x*y^4 - 4*y^5 - 4*x^4*z + 4*x^3*y*z + 5*x^2*y^2*z - 5*x*y^3*z + 2*y^4*z - 5*x^3*z^2 + x^2*y*z^2 + 4*x*y^2*z^2 - 3*y^3*z^2 - 5*x^2*z^3 + 5*x*y*z^3 + 4*x*z^4 + 4*y*z^4 + 5*z^5 - x^4 + 2*x^3*y - 3*x^2*y^2 - 5*x*y^3 - 3*y^4 - 5*x^3*z - 5*x^2*y*z - y^3*z + 2*x^2*z^2 + 5*y^2*z^2 - 2*x*z^3 + y*z^3 + 5*z^4 - 3*x^2*y - 3*x*y^2 + 5*x^2*z + 2*x*y*z + 5*x*z^2]
PASS (K) L0_1 + (x^4): a triple of local length 38 (stable N = 10) <= 38  [175.7s]
     triple: [3*x^4*y - 4*x^3*y^2 - 4*x^2*y^3 + 5*x*y^4 - 2*y^5 - 2*x^4*z + 5*x^3*y*z - 4*x^2*y^2*z + 5*x*y^3*z + 2*y^4*z + x^3*z^2 - 5*x^2*y*z^2 + 4*x*y^2*z^2 + 3*y^3*z^2 - 2*x^2*z^3 + x*y*z^3 + 3*y^2*z^3 + 2*x*z^4 + 4*y*z^4 - 4*z^5 + 3*x^4 + 2*x^2*y^2 + 5*x*y^3 - 2*x^3*z + 5*x^2*y*z - 2*x*y^2*z + 4*y^3*z - 4*x^2*z^2 - 2*x*y*z^2 - y^2*z^2 + 5*x*z^3 - y*z^3 - 3*z^4 - x^2*y + 5*x*y^2 - 5*x^2*z + 5*x*y*z + 2*x*z^2, 2*x^5 + 4*x^4*y + 2*x^3*y^2 - 3*x^2*y^3 - 4*x*y^4 + 4*y^5 + 3*x^4*z + 3*x^3*y*z + 3*x^2*y^2*z + 5*x*y^3*z - 5*y^4*z + x^3*z^2 - x^2*y*z^2 - 4*x*y^2*z^2 + y^3*z^2 - 2*x^2*z^3 - 3*x*y*z^3 + 5*y^2*z^3 - 5*x*z^4 + 5*y*z^4 - 2*z^5 + 4*x^4 - 4*x^3*y - 7*x^2*y^2 - x^2*y*z + 3*x*y^2*z - y^3*z + 3*x^2*z^2 + 8*x*y*z^2 - 5*x*z^3 + 3*y*z^3 + 3*z^4 - 5*x^2*y - 5*x*y^2 + 3*x^2*z - 3*x*y*z + 2*x*z^2, 3*x^5 + 2*x^4*y + 4*x^3*y^2 - 5*x^2*y^3 + 3*x*y^4 - y^5 - 2*x^4*z + 2*x^3*y*z + 2*x^2*y^2*z - 3*y^4*z + x^3*z^2 + 5*x^2*y*z^2 + 2*x*y^2*z^2 - 4*y^3*z^2 - x^2*z^3 + 3*x*y*z^3 - 5*y^2*z^3 + 2*x*z^4 + y*z^4 - 4*z^5 + 2*x^4 + 5*x^3*y + 6*x^2*y^2 - 2*x*y^3 - 3*x^3*z - x*y^2*z + 5*x*y*z^2 + 4*y^2*z^2 - 4*x*z^3 + 4*y*z^3 - 4*z^4 - x^2*y + 4*x*y^2 + 5*x^2*z + 3*x*z^2]
PASS (K) L0_2 + (x^4): a triple of local length 39 (stable N = 10) <= 39  [207.4s]
     triple: [-x^5 - 3*x^4*y + 4*x^3*y^2 - 2*x^2*y^3 - x*y^4 + x^4*z - x^3*y*z - 3*x^2*y^2*z + 5*x*y^3*z + y^4*z - 4*x^3*z^2 + 4*x^2*y*z^2 - 3*x*y^2*z^2 - y^3*z^2 + x^2*z^3 - 3*x*y*z^3 + 2*y^2*z^3 - 4*y*z^4 + 2*z^5 - x^4 - x^3*y + 6*x^2*y^2 + 2*x*y^3 - 4*x^3*z + 4*x^2*y*z - 5*x*y^2*z - 3*x^2*z^2 + 3*x*y*z^2 + 2*y^2*z^2 + 5*x*z^3 + 3*y*z^3 - 2*z^4 + 3*x^2*y + 3*x*y^2 - 5*x^2*z - 5*x*y*z - x*z^2, 5*x^4*y + 2*x^2*y^3 + 2*y^5 + 4*x^4*z - 2*x^3*y*z - 2*x^2*y^2*z + x*y^3*z + y^4*z - 5*x^3*z^2 - x^2*y*z^2 - 3*x*y^2*z^2 - 2*y^3*z^2 + 2*x^2*z^3 + 3*x*y*z^3 + 3*x*z^4 + 5*y*z^4 - 4*z^5 + 5*x^4 + x^3*y - 3*x^2*y^2 - 4*x*y^3 - 3*x^3*z - 8*x^2*y*z + 8*x*y^2*z - 6*x^2*z^2 + 6*x*y*z^2 - 4*y^2*z^2 - 4*x*z^3 - 5*y*z^3 + 3*z^4 + 5*x^2*y - 4*x*y^2 - 2*x^2*z + 5*x*y*z + 4*x*z^2, -4*x^4*y + 4*x^3*y^2 - 3*x^2*y^3 + 3*y^5 - 4*x^4*z - 3*x^3*y*z + 3*x^2*y^2*z - 4*x^3*z^2 + 2*x^2*y*z^2 - x*y^2*z^2 + 4*y^3*z^2 - 5*x^2*z^3 + 5*x*y*z^3 + 2*x*z^4 - 3*y*z^4 - 2*z^5 - 3*x^4 + x^3*y + 4*x^2*y^2 - 5*x*y^3 - x^3*z + x^2*y*z - 2*x*y^2*z - 3*x^2*z^2 - 5*x*y*z^2 + 2*y^2*z^2 - 5*x*z^3 - 2*y*z^3 - 4*z^4 - 2*x^2*y + 4*x^2*z + 5*x*z^2]
PASS (K) L0_3 + (x^4): a triple of local length 40 (stable N = 10) <= 40  [238.7s]
     triple: [-x^5 + 3*x^4*y - x^3*y^2 + 5*x^2*y^3 - 3*x*y^4 + 2*y^5 - 5*x^4*z - x^3*y*z - 5*x^2*y^2*z + 4*y^4*z - x^3*z^2 - 5*x^2*y*z^2 - 4*x*y^2*z^2 + 2*y^3*z^2 + 5*x^2*z^3 - 5*x*y*z^3 - 5*x*z^4 - 3*y*z^4 + 4*z^5 - 4*x^4 - 2*x^3*y + x^2*y^2 - 4*x*y^3 + 5*x^3*z + 3*x^2*y*z - 2*x*y^2*z - 2*x^2*z^2 - 7*x*y*z^2 - 2*x*z^3 - y*z^3 + 3*z^4 + 4*x^2*y + 4*x*y^2 - 3*x^2*z + 4*x*y*z + 5*x*z^2, -4*x^5 - x^4*y + x^3*y^2 - 3*x^2*y^3 - 3*x*y^4 + 2*y^5 + 5*x^4*z + 5*x^3*y*z + 2*x^2*y^2*z + 5*x*y^3*z + 3*y^4*z + 2*x^3*z^2 + 4*x^2*y*z^2 + 2*x*y^2*z^2 - 3*y^3*z^2 + 5*x^2*z^3 + x*y*z^3 - y^2*z^3 + 5*x*z^4 + 5*y*z^4 + 3*x^4 + 2*x^3*y + 4*x^2*y^2 - 2*x*y^3 + 4*x^3*z + 5*x^2*y*z + 2*x*y^2*z + 5*x^2*z^2 + 5*x*y*z^2 - x*z^3 + 5*y*z^3 + z^4 + 3*x^2*y - 5*x*y^2 - 2*x^2*z + 5*x*y*z + 4*x*z^2, x^5 + 3*x^4*y - 5*x^3*y^2 + 4*x^2*y^3 + x*y^4 - 5*y^5 + 5*x^4*z - 5*x^3*y*z + x^2*y^2*z - 5*x*y^3*z - 3*y^4*z - 3*x^3*z^2 - x^2*y*z^2 - 5*x*y^2*z^2 - 5*y^3*z^2 - 3*x*y*z^3 - 5*y^2*z^3 - x*z^4 + 2*y*z^4 - z^5 + 5*x^4 + 2*x^3*y + 5*x^2*y^2 + x*y^3 - 4*x^3*z - 3*x^2*y*z + 5*x*y^2*z + 5*x^2*z^2 - 3*x*y*z^2 + 3*x*z^3 + 3*y*z^3 + z^4 + 2*x^2*y - 3*x*y^2 + 2*x^2*z + 3*x*y*z - 3*x*z^2]
PASS (M) V = <X^5, Y^5 + Y^2Z^3>: closed, H = [1, 3, 6, 6, 3, 2], three general elements of N(D) in Ann(M), local length 38 (stable N = 9)  [252.3s]
PASS (M) V = <X^5 + Y^5, Z^5>: closed, H = [1, 3, 6, 6, 3, 2], three general elements of N(D) in Ann(M), local length 40 (stable N = 10)  [267.8s]
PASS (M) V binary <Y^5 + Z^5, Y^4Z>: closed, H = [1, 3, 6, 6, 3, 2], three general elements of N(D) in Ann(M), local length 40 (stable N = 10)  [287.1s]
PASS (M) V binary <Y^5, Z^5>: closed, H = [1, 3, 6, 6, 3, 2], three general elements of N(D) in Ann(M), local length 39 (stable N = 10)  [310.6s]
  (ON) e(x(x,z)m + y^(delta-mu) z^mu (y,z)^(4-delta) + m^5) by (delta, mu), one random triple each (upper bounds): {(0, 0): 37, (1, 0): 38, (1, 1): 40, (2, 0): 39, (2, 1): 41, (2, 2): 41, (3, 0): 40, (3, 1): 42, (3, 2): 42, (3, 3): 42, (4, 0): 41, (4, 1): 43, (4, 2): 43, (4, 3): 43, (4, 4): 43}
total time 518.6 s
ALL CHECKS PASSED
