  [ok] (Tc) R = Z^4: S_1 o W in D_3 (W = Y^4)
  [ok] (Tc) R = Z^4: for every t != 0, the diagonal change Y -> lambda Y with lambda^4 = 1/t maps R + tW to a multiple of the certified representative Y^4 + Z^4 and preserves X^4, X^3Y, D_3, D_5 and X^6 (an identity modulo that relation; class U)
  [ok] (Tc) R = Z^4: 3 actual free algebras (dim M' = 20) of 3 tries; M_t closed with H and D_4(t) for t = 1, 2 on 3 of 3
  [ok] (Tc) R = Y^4: S_1 o W in D_3 (W = Z^4)
  [ok] (Tc) R = Y^4: for every t != 0, the diagonal change Y -> lambda Y with lambda^4 = t maps R + tW to a multiple of the certified representative Y^4 + Z^4 and preserves X^4, X^3Y, D_3, D_5 and X^6 (an identity modulo that relation; class U)
  [ok] (Tc) R = Y^4: 3 actual free algebras (dim M' = 20) of 3 tries; M_t closed with H and D_4(t) for t = 1, 2 on 3 of 3
  [ok] (Tc) R = X^2Y^2: S_1 o W in D_3 (W = Z^4)
  [ok] (Tc) R = X^2Y^2: for every t != 0, the diagonal change X -> lambda X with lambda^2 = t maps R + tW to a multiple of the certified representative X^2*Y^2 + Z^4 and preserves X^4, X^3Y, D_3, D_5 and X^6 (an identity modulo that relation; class U)
  [ok] (Tc) R = X^2Y^2: 3 actual free algebras (dim M' = 20) of 3 tries; M_t closed with H and D_4(t) for t = 1, 2 on 3 of 3
  [ok] (Tx) R = X^3Z: S_1 o W in D_3 (W = Y^4)
  [ok] (Tx) R = X^3Z: for every t != 0, the diagonal change X -> lambda X with lambda^3 = t maps R + tW to a multiple of the certified representative Y^4 + X^3*Z and preserves X^4, X^3Y, D_3, D_5 and X^6 (an identity modulo that relation; class U)
  [ok] (Tx) R = X^3Z: 3 actual free algebras (dim M' = 20) of 23 tries; M_t closed with H and D_4(t) for t = 1, 2 on 3 of 3
  [ok] (Tx) R = Y^4: S_1 o W in D_3 (W = X^3*Z)
  [ok] (Tx) R = Y^4: for every t != 0, the diagonal change X -> lambda X with lambda^3 = 1/t maps R + tW to a multiple of the certified representative Y^4 + X^3*Z and preserves X^4, X^3Y, D_3, D_5 and X^6 (an identity modulo that relation; class U)
  [ok] (Tx) R = Y^4: 3 actual free algebras (dim M' = 20) of 21 tries; M_t closed with H and D_4(t) for t = 1, 2 on 3 of 3
  [ok] (Tx) R = X^2Y^2: S_1 o W in D_3 (W = X^3*Z)
  [ok] (Tx) R = X^2Y^2: for every t != 0, the diagonal change X -> lambda X with lambda^1 = 1/t maps R + tW to a multiple of the certified representative X^2*Y^2 + X^3*Z and preserves X^4, X^3Y, D_3, D_5 and X^6 (an identity modulo that relation; class U)
  [ok] (Tx) R = X^2Y^2: 3 actual free algebras (dim M' = 20) of 13 tries; M_t closed with H and D_4(t) for t = 1, 2 on 3 of 3
  [ok] (F8) R = X^3Z: S_1 o W in D_3 (W = Z^4)
  [ok] (F8) R = X^3Z: for every t != 0, the diagonal change X -> lambda X with lambda^3 = t maps R + tW to a multiple of the certified representative X^3*Z + Z^4 and preserves X^4, X^3Y, D_3, D_5 and X^6 (an identity modulo that relation; class U)
  [ok] (F8) R = X^3Z: 2 actual free algebras (dim M' = 20) of 30 tries; M_t closed with H and D_4(t) for t = 1, 2 on 2 of 2
  [ok] (F4) S_1 o Y^3Z in D_3 = C[X,Y]_3 + C Y^2Z
  [ok] (F4) identically in QQ[a, b, c, t, 1/t]: (a X^2Y^2 + b XY^3 + c Y^4 + t Y^3Z)(Z -> Z - (bX + cY)/t) = a X^2Y^2 + t Y^3Z, and the change fixes X^4, X^3Y, X^5, X^4Y, X^6 and maps D_3 = C[X,Y]_3 + C Y^2Z to itself (class U)
  [ok] (F4) (S) for R = l X^2Y^2 + XY^3 + Y^4 (l = 0, 1, 17/5), Y^4, X^2Y^2 and t = 1, 2, -3: Z -> Z - (aX + bY)/t maps R + tY^3Z to rho X^2Y^2 + tY^3Z mod <X^4, X^3Y> (a (Ty) datum)
  [ok] (F4) R = (17/5)X^2Y^2 + XY^3 + Y^4: 2 actual free algebras of 2 tries; M_t closed with H and D_4(t) for t = 1, 2 on 2 of 2
  [ok] (F4) R = Y^4: 2 actual free algebras of 2 tries; M_t closed with H and D_4(t) for t = 1, 2 on 2 of 2
  [ok] (F4) R = X^2Y^2: 2 actual free algebras of 2 tries; M_t closed with H and D_4(t) for t = 1, 2 on 2 of 2
accepted free samples: 26
27 checks, 0 failed
ALL CHECKS PASSED
