(U1) Macaulay bound
  [ok] 4^<3> = 5
(U2) closedness: y o P, z o P binary
  [ok] solution space = C[X,Y]_5 + C X^4 Z (dimension 7)
(S) actual algebras in normal form
    sample 0: H ok; smallest k with X^k in M, not in N_X o M: 4
  [ok] sample 0: X^4 in M and X^4 not in N_X o M
    sample 1: H ok; smallest k with X^k in M, not in N_X o M: 4
  [ok] sample 1: X^4 in M and X^4 not in N_X o M
    sample 2: H ok; smallest k with X^k in M, not in N_X o M: 4
  [ok] sample 2: X^4 in M and X^4 not in N_X o M
    sample 3: H ok; smallest k with X^k in M, not in N_X o M: 4
  [ok] sample 3: X^4 in M and X^4 not in N_X o M
    sample 4: H ok; smallest k with X^k in M, not in N_X o M: 4
  [ok] sample 4: X^4 in M and X^4 not in N_X o M
    sample 5: H ok; smallest k with X^k in M, not in N_X o M: 4
  [ok] sample 5: X^4 in M and X^4 not in N_X o M
    sample 6: H ok; smallest k with X^k in M, not in N_X o M: 4
  [ok] sample 6: X^4 in M and X^4 not in N_X o M
    sample 7: H ok; smallest k with X^k in M, not in N_X o M: 4
  [ok] sample 7: X^4 in M and X^4 not in N_X o M
    accepted samples: 8
  [ok] at least 4 accepted samples
11 checks, 0 failed
ALL CHECKS PASSED
