0123_0321_2103<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 21, 70, 204, 560, 1617, 4796, 14249, 41939, 122658, 358991, 1053628, 3095381, 9089525, 26674879, 78271099, 229705211, 674214603, 1978919196, 5808153968, 17046573229, 50030848109, 146839772058, 430974323821, 1264905691383, 3712476662089, 10896049867698, 31979726638169, 93860023381304, 275477780682240, 808523048539737, 2373002454185754, 6964725096985187, 20441360292014808, 59995076923536272, 176084622918073964, 516805639041619206, 1516816537176593316, 4451833031866111950, 13066060994044026425, 38348686637387384655, 112552801197306472096, 330340727738892711006, 969544918062829973355, 2845599314331714523510, 8351789904162283880060, 24512373983486623629796, 71943437894291894217633, 211152875665786797946982, 619730418889505930148663, 1818899178568701819298007, 5338440910687301258293778, 15668241369603141782688697, 45986045686899066819563868, 134968331673857694552937649, 396129962529735379756526167, 1162635303169044352072766829, 3412316603223933464366054097, 10015096366760007738372426993, 29394152682292644788601662769, 86271382747513860946813010740, 253205171845349783875877127166, 743153256704704427999818784155, 2181143295477838825958816170839, 6401621781896139521589044146518, 18788660755766279951260590566493, 55144428243730429967556962209151, 161848042596366366983881007567351, 475021497666056177866068401473226, 1394180736603908406053240458532415, 4091898863246565661138187807499672, 12009659771820148451962389710837702, 35248165376316198512501523217396523, 103452819313951018759791225017624846, 303632421992554713967690926338560681, 891156454666405404276914192186700028, 2615530388625857786803924120694330668, 7676541170748949394425078612822588756, 22530529410963488156460162312322730714, 66126754777603198789579713587703621950, 194081000834781214913363223367057766880, 569624730741937429610141747224517807213, 1671839760085759507323636395533704827795, 4906823795664653948556735773045690728094, 14401451823628013387331765999331538668162, 42268037994664736884599582700002762641915, 124056036696746372176791451154682711323036, 364102545825454813600260810971873165483238, 1068635331311163547492058137885638430918654, 3136428142070637201598834563776808069215279, 9205368007347208149351617581221086054624252, 27017612491752428959999548280121990641790115, 79296274105705568956564205249376448261165133, 232733336040209927956764234817241156101873700, 683068735766842058663655901680461429978830183, 2004796157356242194908011388951229953101684640, 5884045663483955133577697583525712151888471369, 17269582866529898118377593082022010243274250647<br /><br />


Generating function in Maple syntax:<br />
-(x^5+x^3+x^2+x-1)/(x^12+16*x^11+10*x^10+17*x^9+25*x^8+25*x^7-7*x^6-14*x^5-5*x^4-2*x^3-x^2-2*x+1)<br /><br />



Generating function in latex syntax:<br />
-\frac{x^{5}+x^{3}+x^{2}+x -1}{x^{12}+16 x^{11}+10 x^{10}+17 x^{9}+25 x^{8}+25 x^{7}-7 x^{6}-14 x^{5}-5 x^{4}-2 x^{3}-x^{2}-2 x +1}<br /><br />



Generating function in sympy syntax:<br />
(-x**5 - x**3 - x**2 - x + 1)/(x**12 + 16*x**11 + 10*x**10 + 17*x**9 + 25*x**8 + 25*x**7 - 7*x**6 - 14*x**5 - 5*x**4 - 2*x**3 - x**2 - 2*x + 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^12+16*x^11+10*x^10+17*x^9+25*x^8+25*x^7-7*x^6-14*x^5-5*x^4-2*x^3-x^2-2*x+1)*F(x)+x^5+x^3+x^2+x-1 = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{12}+16 x^{11}+10 x^{10}+17 x^{9}+25 x^{8}+25 x^{7}-7 x^{6}-14 x^{5}-5 x^{4}-2 x^{3}-x^{2}-2 x +1\right) F \! \left(x \right)+x^{5}+x^{3}+x^{2}+x -1 = 0<br /><br />



Explicit closed form in Maple syntax:<br />
-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+10)-22796455585348217604433870077/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+10)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+9)-791069925316839079470365582251/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+9)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+8)-729154296992573955173243115733/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+8)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+7)-1680588922039610778291890561927/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+7)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+6)-2658332629739796708329781472131/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+6)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+5)-1794360943665358179694705358603/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+5)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+4)-872436660156731014292224910275/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+4)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+3)-100042123421401122240198914393/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+3)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+2)+245625423704534395055094747636/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+2)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n+1)+346181722267385081286400562078/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n+1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n-1)+281471904417498036418670920669/7946208556085613445891636877482*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n-1)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 1)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 2)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 3)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 4)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 5)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 6)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 7)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 8)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 9)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 10)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 11)^(-n)+655914691762672849937133397022/3973104278042806722945818438741*RootOf(_Z^12+16*_Z^11+10*_Z^10+17*_Z^9+25*_Z^8+25*_Z^7-7*_Z^6-14*_Z^5-5*_Z^4-2*_Z^3-_Z^2-2*_Z+1,index = 12)^(-n)<br /><br />



Explicit closed form in latex syntax:<br />
-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =10\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =11\right)^{-n +10}}{3973104278042806722945818438741}-\frac{22796455585348217604433870077 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =12\right)^{-n +10}}{3973104278042806722945818438741}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =10\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =11\right)^{-n +9}}{7946208556085613445891636877482}-\frac{791069925316839079470365582251 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =12\right)^{-n +9}}{7946208556085613445891636877482}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +8}}{3973104278042806722945818438741}-\frac{729154296992573955173243115733 \mathit{RootOf}\! 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\left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +7}}{7946208556085613445891636877482}-\frac{1680588922039610778291890561927 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +7}}{7946208556085613445891636877482}-\frac{1680588922039610778291890561927 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +7}}{7946208556085613445891636877482}-\frac{1680588922039610778291890561927 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +7}}{7946208556085613445891636877482}-\frac{1680588922039610778291890561927 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +7}}{7946208556085613445891636877482}-\frac{1680588922039610778291890561927 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +7}}{7946208556085613445891636877482}-\frac{1680588922039610778291890561927 \mathit{RootOf}\! 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\left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =10\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =11\right)^{-n +2}}{3973104278042806722945818438741}+\frac{245625423704534395055094747636 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =12\right)^{-n +2}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =10\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =11\right)^{-n +1}}{3973104278042806722945818438741}+\frac{346181722267385081286400562078 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =12\right)^{-n +1}}{3973104278042806722945818438741}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =9\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =10\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =11\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =12\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{7946208556085613445891636877482}+\frac{281471904417498036418670920669 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{7946208556085613445891636877482}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =9\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =10\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =11\right)^{-n}}{3973104278042806722945818438741}+\frac{655914691762672849937133397022 \mathit{RootOf}\! \left(\textit{\_Z}^{12}+16 \textit{\_Z}^{11}+10 \textit{\_Z}^{10}+17 \textit{\_Z}^{9}+25 \textit{\_Z}^{8}+25 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1, \mathit{index} =12\right)^{-n}}{3973104278042806722945818438741}<br /><br />



  
    Recurrence in maple format:<br />
    
      a(0) = 1<br />
    
      a(1) = 1<br />
    
      a(2) = 2<br />
    
      a(3) = 6<br />
    
      a(4) = 21<br />
    
      a(5) = 70<br />
    
      a(6) = 204<br />
    
      a(7) = 560<br />
    
      a(8) = 1617<br />
    
      a(9) = 4796<br />
    
      a(10) = 14249<br />
    
      a(11) = 41939<br />
    
    a(n+12) = -a(n)-16*a(n+1)-10*a(n+2)-17*a(n+3)-25*a(n+4)-25*a(n+5)+7*a(n+6)+14*a(n+7)+5*a(n+8)+2*a(n+9)+a(n+10)+2*a(n+11), n >= 12<br /><br />

    Recurrence in latex format:<br />
    
      a \! \left(0\right) = 1<br />
    
      a \! \left(1\right) = 1<br />
    
      a \! \left(2\right) = 2<br />
    
      a \! \left(3\right) = 6<br />
    
      a \! \left(4\right) = 21<br />
    
      a \! \left(5\right) = 70<br />
    
      a \! \left(6\right) = 204<br />
    
      a \! \left(7\right) = 560<br />
    
      a \! \left(8\right) = 1617<br />
    
      a \! \left(9\right) = 4796<br />
    
      a \! \left(10\right) = 14249<br />
    
      a \! \left(11\right) = 41939<br />
    
    a \! \left(n +12\right) = -a \! \left(n \right)-16 a \! \left(n +1\right)-10 a \! \left(n +2\right)-17 a \! \left(n +3\right)-25 a \! \left(n +4\right)-25 a \! \left(n +5\right)+7 a \! \left(n +6\right)+14 a \! \left(n +7\right)+5 a \! \left(n +8\right)+2 a \! \left(n +9\right)+a \! \left(n +10\right)+2 a \! \left(n +11\right), \quad n \geq 12<br /><br />
  



  Specification 1<br />
  Strategy pack name: point_placements<br />
  Tree: http://permpal.com/tree/14654/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[3,x]<br />
  
    F[3,x] = F[4,x]*F[5,x]<br />
  
    F[4,x] = x<br />
  
    F[5,x] = F[29,x]+F[6,x]<br />
  
    F[6,x] = F[1,x]+F[7,x]<br />
  
    F[7,x] = F[8,x]<br />
  
    F[8,x] = F[4,x]*F[9,x]<br />
  
    F[9,x] = F[10,x]+F[14,x]<br />
  
    F[10,x] = F[1,x]+F[11,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[13,x]*F[4,x]<br />
  
    F[13,x] = F[1,x]+F[4,x]<br />
  
    F[14,x] = F[15,x]+F[17,x]<br />
  
    F[15,x] = F[16,x]<br />
  
    F[16,x] = F[13,x]*F[4,x]<br />
  
    F[17,x] = F[18,x]+F[19,x]+F[24,x]<br />
  
    F[18,x] = 0<br />
  
    F[19,x] = F[20,x]*F[4,x]<br />
  
    F[20,x] = F[11,x]+F[21,x]<br />
  
    F[21,x] = F[22,x]<br />
  
    F[22,x] = F[23,x]*F[4,x]<br />
  
    F[23,x] = F[4,x]<br />
  
    F[24,x] = F[25,x]*F[4,x]<br />
  
    F[25,x] = F[15,x]+F[26,x]<br />
  
    F[26,x] = F[27,x]<br />
  
    F[27,x] = F[28,x]*F[4,x]<br />
  
    F[28,x] = F[4,x]<br />
  
    F[29,x] = F[2,x]+F[30,x]<br />
  
    F[30,x] = F[171,x]+F[18,x]+F[31,x]<br />
  
    F[31,x] = F[32,x]*F[4,x]<br />
  
    F[32,x] = F[33,x]+F[55,x]<br />
  
    F[33,x] = F[34,x]+F[7,x]<br />
  
    F[34,x] = F[18,x]+F[35,x]+F[46,x]<br />
  
    F[35,x] = F[36,x]*F[4,x]<br />
  
    F[36,x] = F[37,x]+F[39,x]<br />
  
    F[37,x] = F[11,x]+F[38,x]<br />
  
    F[38,x] = F[22,x]<br />
  
    F[39,x] = F[40,x]+F[43,x]<br />
  
    F[40,x] = F[41,x]<br />
  
    F[41,x] = F[4,x]*F[42,x]<br />
  
    F[42,x] = F[15,x]<br />
  
    F[43,x] = F[44,x]<br />
  
    F[44,x] = F[4,x]*F[45,x]<br />
  
    F[45,x] = F[26,x]<br />
  
    F[46,x] = F[4,x]*F[47,x]<br />
  
    F[47,x] = F[14,x]+F[48,x]<br />
  
    F[48,x] = F[49,x]+F[50,x]<br />
  
    F[49,x] = F[27,x]<br />
  
    F[50,x] = 2*F[18,x]+F[51,x]+F[53,x]<br />
  
    F[51,x] = F[4,x]*F[52,x]<br />
  
    F[52,x] = F[21,x]<br />
  
    F[53,x] = F[4,x]*F[54,x]<br />
  
    F[54,x] = F[49,x]<br />
  
    F[55,x] = F[56,x]+F[79,x]<br />
  
    F[56,x] = F[57,x]<br />
  
    F[57,x] = F[4,x]*F[58,x]<br />
  
    F[58,x] = F[59,x]+F[65,x]<br />
  
    F[59,x] = F[2,x]+F[60,x]<br />
  
    F[60,x] = F[61,x]<br />
  
    F[61,x] = F[4,x]*F[62,x]<br />
  
    F[62,x] = F[2,x]+F[63,x]<br />
  
    F[63,x] = F[64,x]<br />
  
    F[64,x] = F[2,x]*F[4,x]<br />
  
    F[65,x] = F[66,x]+F[68,x]<br />
  
    F[66,x] = F[67,x]<br />
  
    F[67,x] = F[4,x]*F[62,x]<br />
  
    F[68,x] = 2*F[18,x]+F[69,x]+F[74,x]<br />
  
    F[69,x] = F[4,x]*F[70,x]<br />
  
    F[70,x] = F[60,x]+F[71,x]<br />
  
    F[71,x] = F[72,x]<br />
  
    F[72,x] = F[4,x]*F[73,x]<br />
  
    F[73,x] = F[63,x]<br />
  
    F[74,x] = F[4,x]*F[75,x]<br />
  
    F[75,x] = F[66,x]+F[76,x]<br />
  
    F[76,x] = F[77,x]<br />
  
    F[77,x] = F[4,x]*F[78,x]<br />
  
    F[78,x] = F[63,x]<br />
  
    F[79,x] = 2*F[18,x]+F[154,x]+F[80,x]<br />
  
    F[80,x] = F[4,x]*F[81,x]<br />
  
    F[81,x] = F[147,x]+F[82,x]<br />
  
    F[82,x] = F[60,x]+F[83,x]<br />
  
    F[83,x] = F[84,x]<br />
  
    F[84,x] = F[4,x]*F[85,x]<br />
  
    F[85,x] = F[86,x]<br />
  
    F[86,x] = F[18,x]+F[64,x]+F[87,x]<br />
  
    F[87,x] = F[4,x]*F[88,x]<br />
  
    F[88,x] = F[101,x]+F[89,x]<br />
  
    F[89,x] = F[4,x]+F[90,x]<br />
  
    F[90,x] = F[18,x]+F[91,x]+F[98,x]<br />
  
    F[91,x] = F[4,x]*F[92,x]<br />
  
    F[92,x] = F[93,x]+F[96,x]<br />
  
    F[93,x] = F[4,x]+F[94,x]<br />
  
    F[94,x] = F[95,x]<br />
  
    F[95,x] = x^2<br />
  
    F[96,x] = F[97,x]+F[99,x]<br />
  
    F[97,x] = F[98,x]<br />
  
    F[98,x] = F[15,x]*F[4,x]<br />
  
    F[99,x] = F[100,x]<br />
  
    F[100,x] = F[26,x]*F[4,x]<br />
  
    F[101,x] = F[102,x]+F[63,x]<br />
  
    F[102,x] = 2*F[18,x]+F[103,x]+F[110,x]<br />
  
    F[103,x] = F[104,x]*F[4,x]<br />
  
    F[104,x] = F[105,x]+F[108,x]<br />
  
    F[105,x] = F[106,x]+F[63,x]<br />
  
    F[106,x] = F[107,x]<br />
  
    F[107,x] = F[4,x]*F[86,x]<br />
  
    F[108,x] = F[109,x]+F[132,x]<br />
  
    F[109,x] = F[110,x]<br />
  
    F[110,x] = F[111,x]*F[4,x]<br />
  
    F[111,x] = F[112,x]+F[130,x]+F[18,x]<br />
  
    F[112,x] = F[113,x]*F[4,x]<br />
  
    F[113,x] = F[114,x]+F[122,x]<br />
  
    F[114,x] = F[115,x]+F[15,x]<br />
  
    F[115,x] = F[116,x]+F[18,x]+F[91,x]<br />
  
    F[116,x] = F[117,x]*F[4,x]<br />
  
    F[117,x] = F[118,x]+F[15,x]<br />
  
    F[118,x] = F[119,x]+F[18,x]+F[98,x]<br />
  
    F[119,x] = F[120,x]*F[4,x]<br />
  
    F[120,x] = F[121,x]+F[4,x]<br />
  
    F[121,x] = F[95,x]<br />
  
    F[122,x] = F[123,x]+F[66,x]<br />
  
    F[123,x] = 2*F[18,x]+F[103,x]+F[124,x]<br />
  
    F[124,x] = F[125,x]*F[4,x]<br />
  
    F[125,x] = F[111,x]+F[126,x]<br />
  
    F[126,x] = 2*F[18,x]+F[110,x]+F[127,x]<br />
  
    F[127,x] = F[128,x]*F[4,x]<br />
  
    F[128,x] = F[129,x]+F[63,x]<br />
  
    F[129,x] = F[107,x]<br />
  
    F[130,x] = F[131,x]*F[4,x]<br />
  
    F[131,x] = F[2,x]+F[86,x]<br />
  
    F[132,x] = F[133,x]<br />
  
    F[133,x] = F[134,x]*F[4,x]<br />
  
    F[134,x] = 2*F[18,x]+F[135,x]+F[145,x]<br />
  
    F[135,x] = F[136,x]*F[4,x]<br />
  
    F[136,x] = F[137,x]+F[141,x]<br />
  
    F[137,x] = F[138,x]+F[26,x]<br />
  
    F[138,x] = F[139,x]<br />
  
    F[139,x] = F[140,x]*F[4,x]<br />
  
    F[140,x] = F[97,x]<br />
  
    F[141,x] = F[142,x]+F[76,x]<br />
  
    F[142,x] = F[143,x]<br />
  
    F[143,x] = F[144,x]*F[4,x]<br />
  
    F[144,x] = F[109,x]<br />
  
    F[145,x] = F[146,x]*F[4,x]<br />
  
    F[146,x] = F[63,x]<br />
  
    F[147,x] = F[148,x]+F[151,x]<br />
  
    F[148,x] = F[149,x]<br />
  
    F[149,x] = F[150,x]*F[4,x]<br />
  
    F[150,x] = F[111,x]<br />
  
    F[151,x] = F[152,x]<br />
  
    F[152,x] = F[153,x]*F[4,x]<br />
  
    F[153,x] = F[134,x]<br />
  
    F[154,x] = F[155,x]*F[4,x]<br />
  
    F[155,x] = F[156,x]+F[164,x]<br />
  
    F[156,x] = F[111,x]+F[157,x]<br />
  
    F[157,x] = 2*F[18,x]+F[158,x]+F[161,x]<br />
  
    F[158,x] = F[159,x]*F[4,x]<br />
  
    F[159,x] = F[160,x]+F[60,x]<br />
  
    F[160,x] = F[84,x]<br />
  
    F[161,x] = F[162,x]*F[4,x]<br />
  
    F[162,x] = F[111,x]+F[163,x]<br />
  
    F[163,x] = F[145,x]<br />
  
    F[164,x] = F[165,x]+F[166,x]<br />
  
    F[165,x] = F[145,x]<br />
  
    F[166,x] = 3*F[18,x]+F[167,x]+F[169,x]<br />
  
    F[167,x] = F[168,x]*F[4,x]<br />
  
    F[168,x] = F[71,x]<br />
  
    F[169,x] = F[170,x]*F[4,x]<br />
  
    F[170,x] = F[165,x]<br />
  
    F[171,x] = F[172,x]*F[4,x]<br />
  
    F[172,x] = F[173,x]+F[182,x]<br />
  
    F[173,x] = F[174,x]+F[2,x]<br />
  
    F[174,x] = F[175,x]+F[18,x]+F[181,x]<br />
  
    F[175,x] = F[176,x]*F[4,x]<br />
  
    F[176,x] = F[177,x]+F[179,x]<br />
  
    F[177,x] = F[11,x]+F[178,x]<br />
  
    F[178,x] = F[18,x]+F[24,x]+F[35,x]<br />
  
    F[179,x] = F[180,x]+F[60,x]<br />
  
    F[180,x] = 2*F[18,x]+F[161,x]+F[80,x]<br />
  
    F[181,x] = F[131,x]*F[4,x]<br />
  
    F[182,x] = F[111,x]+F[183,x]<br />
  
    F[183,x] = F[158,x]+F[18,x]+F[184,x]+F[202,x]<br />
  
    F[184,x] = F[185,x]*F[4,x]<br />
  
    F[185,x] = F[186,x]+F[193,x]<br />
  
    F[186,x] = F[17,x]+F[187,x]<br />
  
    F[187,x] = F[18,x]+F[188,x]+F[190,x]+F[53,x]<br />
  
    F[188,x] = F[189,x]*F[4,x]<br />
  
    F[189,x] = F[21,x]<br />
  
    F[190,x] = F[191,x]*F[4,x]<br />
  
    F[191,x] = F[192,x]+F[40,x]<br />
  
    F[192,x] = F[44,x]<br />
  
    F[193,x] = F[194,x]+F[68,x]<br />
  
    F[194,x] = 2*F[18,x]+F[169,x]+F[195,x]+F[197,x]<br />
  
    F[195,x] = F[196,x]*F[4,x]<br />
  
    F[196,x] = F[71,x]<br />
  
    F[197,x] = F[198,x]*F[4,x]<br />
  
    F[198,x] = F[148,x]+F[199,x]<br />
  
    F[199,x] = F[200,x]<br />
  
    F[200,x] = F[201,x]*F[4,x]<br />
  
    F[201,x] = F[163,x]<br />
  
    F[202,x] = F[203,x]*F[4,x]<br />
  
    F[203,x] = F[111,x]+F[134,x]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = x<br />
  
    F_{5}\! \left(x \right) = F_{29}\! \left(x \right)+F_{6}\! \left(x \right)<br />
  
    F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{7}\! \left(x \right) = F_{8}\! \left(x \right)<br />
  
    F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)<br />
  
    F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)<br />
  
    F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)<br />
  
    F_{11}\! \left(x \right) = F_{12}\! \left(x \right)<br />
  
    F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{16}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{24}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = 0<br />
  
    F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)<br />
  
    F_{21}\! \left(x \right) = F_{22}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = F_{4}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)<br />
  
    F_{26}\! \left(x \right) = F_{27}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{4}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{171}\! \left(x \right)+F_{18}\! \left(x \right)+F_{31}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{55}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{46}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{39}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{22}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{41}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{44}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{26}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{14}\! \left(x \right)+F_{48}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{27}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{21}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{49}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{79}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{57}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{65}\! \left(x \right)<br />
  
    F_{59}\! \left(x \right) = F_{2}\! \left(x \right)+F_{60}\! \left(x \right)<br />
  
    F_{60}\! \left(x \right) = F_{61}\! \left(x \right)<br />
  
    F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)<br />
  
    F_{62}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)<br />
  
    F_{63}\! \left(x \right) = F_{64}\! \left(x \right)<br />
  
    F_{64}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)<br />
  
    F_{66}\! \left(x \right) = F_{67}\! \left(x \right)<br />
  
    F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)<br />
  
    F_{68}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{74}\! \left(x \right)<br />
  
    F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)<br />
  
    F_{70}\! \left(x \right) = F_{60}\! \left(x \right)+F_{71}\! \left(x \right)<br />
  
    F_{71}\! \left(x \right) = F_{72}\! \left(x \right)<br />
  
    F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)<br />
  
    F_{73}\! \left(x \right) = F_{63}\! \left(x \right)<br />
  
    F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)<br />
  
    F_{75}\! \left(x \right) = F_{66}\! \left(x \right)+F_{76}\! \left(x \right)<br />
  
    F_{76}\! \left(x \right) = F_{77}\! \left(x \right)<br />
  
    F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)<br />
  
    F_{78}\! \left(x \right) = F_{63}\! \left(x \right)<br />
  
    F_{79}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{154}\! \left(x \right)+F_{80}\! \left(x \right)<br />
  
    F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)<br />
  
    F_{81}\! \left(x \right) = F_{147}\! \left(x \right)+F_{82}\! \left(x \right)<br />
  
    F_{82}\! \left(x \right) = F_{60}\! \left(x \right)+F_{83}\! \left(x \right)<br />
  
    F_{83}\! \left(x \right) = F_{84}\! \left(x \right)<br />
  
    F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)<br />
  
    F_{85}\! \left(x \right) = F_{86}\! \left(x \right)<br />
  
    F_{86}\! \left(x \right) = F_{18}\! \left(x \right)+F_{64}\! \left(x \right)+F_{87}\! \left(x \right)<br />
  
    F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)<br />
  
    F_{88}\! \left(x \right) = F_{101}\! \left(x \right)+F_{89}\! \left(x \right)<br />
  
    F_{89}\! \left(x \right) = F_{4}\! \left(x \right)+F_{90}\! \left(x \right)<br />
  
    F_{90}\! \left(x \right) = F_{18}\! \left(x \right)+F_{91}\! \left(x \right)+F_{98}\! \left(x \right)<br />
  
    F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)<br />
  
    F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{96}\! \left(x \right)<br />
  
    F_{93}\! \left(x \right) = F_{4}\! \left(x \right)+F_{94}\! \left(x \right)<br />
  
    F_{94}\! \left(x \right) = F_{95}\! \left(x \right)<br />
  
    F_{95}\! \left(x \right) = x^{2}<br />
  
    F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)<br />
  
    F_{97}\! \left(x \right) = F_{98}\! \left(x \right)<br />
  
    F_{98}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{99}\! \left(x \right) = F_{100}\! \left(x \right)<br />
  
    F_{100}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{63}\! \left(x \right)<br />
  
    F_{102}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{103}\! \left(x \right)+F_{110}\! \left(x \right)<br />
  
    F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{108}\! \left(x \right)<br />
  
    F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{63}\! \left(x \right)<br />
  
    F_{106}\! \left(x \right) = F_{107}\! \left(x \right)<br />
  
    F_{107}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)<br />
  
    F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{132}\! \left(x \right)<br />
  
    F_{109}\! \left(x \right) = F_{110}\! \left(x \right)<br />
  
    F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{130}\! \left(x \right)+F_{18}\! \left(x \right)<br />
  
    F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{122}\! \left(x \right)<br />
  
    F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{15}\! \left(x \right)<br />
  
    F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{18}\! \left(x \right)+F_{91}\! \left(x \right)<br />
  
    F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{15}\! \left(x \right)<br />
  
    F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{18}\! \left(x \right)+F_{98}\! \left(x \right)<br />
  
    F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{121}\! \left(x \right) = F_{95}\! \left(x \right)<br />
  
    F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{66}\! \left(x \right)<br />
  
    F_{123}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{103}\! \left(x \right)+F_{124}\! \left(x \right)<br />
  
    F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{125}\! \left(x \right) = F_{111}\! \left(x \right)+F_{126}\! \left(x \right)<br />
  
    F_{126}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{110}\! \left(x \right)+F_{127}\! \left(x \right)<br />
  
    F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{63}\! \left(x \right)<br />
  
    F_{129}\! \left(x \right) = F_{107}\! \left(x \right)<br />
  
    F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{131}\! \left(x \right) = F_{2}\! \left(x \right)+F_{86}\! \left(x \right)<br />
  
    F_{132}\! \left(x \right) = F_{133}\! \left(x \right)<br />
  
    F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{134}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{135}\! \left(x \right)+F_{145}\! \left(x \right)<br />
  
    F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{141}\! \left(x \right)<br />
  
    F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{26}\! \left(x \right)<br />
  
    F_{138}\! \left(x \right) = F_{139}\! \left(x \right)<br />
  
    F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{140}\! \left(x \right) = F_{97}\! \left(x \right)<br />
  
    F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{76}\! \left(x \right)<br />
  
    F_{142}\! \left(x \right) = F_{143}\! \left(x \right)<br />
  
    F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{144}\! \left(x \right) = F_{109}\! \left(x \right)<br />
  
    F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{146}\! \left(x \right) = F_{63}\! \left(x \right)<br />
  
    F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{151}\! \left(x \right)<br />
  
    F_{148}\! \left(x \right) = F_{149}\! \left(x \right)<br />
  
    F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{150}\! \left(x \right) = F_{111}\! \left(x \right)<br />
  
    F_{151}\! \left(x \right) = F_{152}\! \left(x \right)<br />
  
    F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{153}\! \left(x \right) = F_{134}\! \left(x \right)<br />
  
    F_{154}\! \left(x \right) = F_{155}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{164}\! \left(x \right)<br />
  
    F_{156}\! \left(x \right) = F_{111}\! \left(x \right)+F_{157}\! \left(x \right)<br />
  
    F_{157}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{158}\! \left(x \right)+F_{161}\! \left(x \right)<br />
  
    F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{60}\! \left(x \right)<br />
  
    F_{160}\! \left(x \right) = F_{84}\! \left(x \right)<br />
  
    F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{162}\! \left(x \right) = F_{111}\! \left(x \right)+F_{163}\! \left(x \right)<br />
  
    F_{163}\! \left(x \right) = F_{145}\! \left(x \right)<br />
  
    F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{166}\! \left(x \right)<br />
  
    F_{165}\! \left(x \right) = F_{145}\! \left(x \right)<br />
  
    F_{166}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{167}\! \left(x \right)+F_{169}\! \left(x \right)<br />
  
    F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{168}\! \left(x \right) = F_{71}\! \left(x \right)<br />
  
    F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{170}\! \left(x \right) = F_{165}\! \left(x \right)<br />
  
    F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{182}\! \left(x \right)<br />
  
    F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{18}\! \left(x \right)+F_{181}\! \left(x \right)<br />
  
    F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{179}\! \left(x \right)<br />
  
    F_{177}\! \left(x \right) = F_{11}\! \left(x \right)+F_{178}\! \left(x \right)<br />
  
    F_{178}\! \left(x \right) = F_{18}\! \left(x \right)+F_{24}\! \left(x \right)+F_{35}\! \left(x \right)<br />
  
    F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{60}\! \left(x \right)<br />
  
    F_{180}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{161}\! \left(x \right)+F_{80}\! \left(x \right)<br />
  
    F_{181}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{182}\! \left(x \right) = F_{111}\! \left(x \right)+F_{183}\! \left(x \right)<br />
  
    F_{183}\! \left(x \right) = F_{158}\! \left(x \right)+F_{18}\! \left(x \right)+F_{184}\! \left(x \right)+F_{202}\! \left(x \right)<br />
  
    F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{193}\! \left(x \right)<br />
  
    F_{186}\! \left(x \right) = F_{17}\! \left(x \right)+F_{187}\! \left(x \right)<br />
  
    F_{187}\! \left(x \right) = F_{18}\! \left(x \right)+F_{188}\! \left(x \right)+F_{190}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
    F_{188}\! \left(x \right) = F_{189}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{189}\! \left(x \right) = F_{21}\! \left(x \right)<br />
  
    F_{190}\! \left(x \right) = F_{191}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{40}\! \left(x \right)<br />
  
    F_{192}\! \left(x \right) = F_{44}\! \left(x \right)<br />
  
    F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{68}\! \left(x \right)<br />
  
    F_{194}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{169}\! \left(x \right)+F_{195}\! \left(x \right)+F_{197}\! \left(x \right)<br />
  
    F_{195}\! \left(x \right) = F_{196}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{196}\! \left(x \right) = F_{71}\! \left(x \right)<br />
  
    F_{197}\! \left(x \right) = F_{198}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{198}\! \left(x \right) = F_{148}\! \left(x \right)+F_{199}\! \left(x \right)<br />
  
    F_{199}\! \left(x \right) = F_{200}\! \left(x \right)<br />
  
    F_{200}\! \left(x \right) = F_{201}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{201}\! \left(x \right) = F_{163}\! \left(x \right)<br />
  
    F_{202}\! \left(x \right) = F_{203}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{203}\! \left(x \right) = F_{111}\! \left(x \right)+F_{134}\! \left(x \right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_3(x))<br />
  
    Eq(F_3(x), F_4(x)*F_5(x))<br />
  
    Eq(F_4(x), x)<br />
  
    Eq(F_5(x), F_29(x) + F_6(x))<br />
  
    Eq(F_6(x), F_1(x) + F_7(x))<br />
  
    Eq(F_7(x), F_8(x))<br />
  
    Eq(F_8(x), F_4(x)*F_9(x))<br />
  
    Eq(F_9(x), F_10(x) + F_14(x))<br />
  
    Eq(F_10(x), F_1(x) + F_11(x))<br />
  
    Eq(F_11(x), F_12(x))<br />
  
    Eq(F_12(x), F_13(x)*F_4(x))<br />
  
    Eq(F_13(x), F_1(x) + F_4(x))<br />
  
    Eq(F_14(x), F_15(x) + F_17(x))<br />
  
    Eq(F_15(x), F_16(x))<br />
  
    Eq(F_16(x), F_13(x)*F_4(x))<br />
  
    Eq(F_17(x), F_18(x) + F_19(x) + F_24(x))<br />
  
    Eq(F_18(x), 0)<br />
  
    Eq(F_19(x), F_20(x)*F_4(x))<br />
  
    Eq(F_20(x), F_11(x) + F_21(x))<br />
  
    Eq(F_21(x), F_22(x))<br />
  
    Eq(F_22(x), F_23(x)*F_4(x))<br />
  
    Eq(F_23(x), F_4(x))<br />
  
    Eq(F_24(x), F_25(x)*F_4(x))<br />
  
    Eq(F_25(x), F_15(x) + F_26(x))<br />
  
    Eq(F_26(x), F_27(x))<br />
  
    Eq(F_27(x), F_28(x)*F_4(x))<br />
  
    Eq(F_28(x), F_4(x))<br />
  
    Eq(F_29(x), F_2(x) + F_30(x))<br />
  
    Eq(F_30(x), F_171(x) + F_18(x) + F_31(x))<br />
  
    Eq(F_31(x), F_32(x)*F_4(x))<br />
  
    Eq(F_32(x), F_33(x) + F_55(x))<br />
  
    Eq(F_33(x), F_34(x) + F_7(x))<br />
  
    Eq(F_34(x), F_18(x) + F_35(x) + F_46(x))<br />
  
    Eq(F_35(x), F_36(x)*F_4(x))<br />
  
    Eq(F_36(x), F_37(x) + F_39(x))<br />
  
    Eq(F_37(x), F_11(x) + F_38(x))<br />
  
    Eq(F_38(x), F_22(x))<br />
  
    Eq(F_39(x), F_40(x) + F_43(x))<br />
  
    Eq(F_40(x), F_41(x))<br />
  
    Eq(F_41(x), F_4(x)*F_42(x))<br />
  
    Eq(F_42(x), F_15(x))<br />
  
    Eq(F_43(x), F_44(x))<br />
  
    Eq(F_44(x), F_4(x)*F_45(x))<br />
  
    Eq(F_45(x), F_26(x))<br />
  
    Eq(F_46(x), F_4(x)*F_47(x))<br />
  
    Eq(F_47(x), F_14(x) + F_48(x))<br />
  
    Eq(F_48(x), F_49(x) + F_50(x))<br />
  
    Eq(F_49(x), F_27(x))<br />
  
    Eq(F_50(x), 2*F_18(x) + F_51(x) + F_53(x))<br />
  
    Eq(F_51(x), F_4(x)*F_52(x))<br />
  
    Eq(F_52(x), F_21(x))<br />
  
    Eq(F_53(x), F_4(x)*F_54(x))<br />
  
    Eq(F_54(x), F_49(x))<br />
  
    Eq(F_55(x), F_56(x) + F_79(x))<br />
  
    Eq(F_56(x), F_57(x))<br />
  
    Eq(F_57(x), F_4(x)*F_58(x))<br />
  
    Eq(F_58(x), F_59(x) + F_65(x))<br />
  
    Eq(F_59(x), F_2(x) + F_60(x))<br />
  
    Eq(F_60(x), F_61(x))<br />
  
    Eq(F_61(x), F_4(x)*F_62(x))<br />
  
    Eq(F_62(x), F_2(x) + F_63(x))<br />
  
    Eq(F_63(x), F_64(x))<br />
  
    Eq(F_64(x), F_2(x)*F_4(x))<br />
  
    Eq(F_65(x), F_66(x) + F_68(x))<br />
  
    Eq(F_66(x), F_67(x))<br />
  
    Eq(F_67(x), F_4(x)*F_62(x))<br />
  
    Eq(F_68(x), 2*F_18(x) + F_69(x) + F_74(x))<br />
  
    Eq(F_69(x), F_4(x)*F_70(x))<br />
  
    Eq(F_70(x), F_60(x) + F_71(x))<br />
  
    Eq(F_71(x), F_72(x))<br />
  
    Eq(F_72(x), F_4(x)*F_73(x))<br />
  
    Eq(F_73(x), F_63(x))<br />
  
    Eq(F_74(x), F_4(x)*F_75(x))<br />
  
    Eq(F_75(x), F_66(x) + F_76(x))<br />
  
    Eq(F_76(x), F_77(x))<br />
  
    Eq(F_77(x), F_4(x)*F_78(x))<br />
  
    Eq(F_78(x), F_63(x))<br />
  
    Eq(F_79(x), F_154(x) + 2*F_18(x) + F_80(x))<br />
  
    Eq(F_80(x), F_4(x)*F_81(x))<br />
  
    Eq(F_81(x), F_147(x) + F_82(x))<br />
  
    Eq(F_82(x), F_60(x) + F_83(x))<br />
  
    Eq(F_83(x), F_84(x))<br />
  
    Eq(F_84(x), F_4(x)*F_85(x))<br />
  
    Eq(F_85(x), F_86(x))<br />
  
    Eq(F_86(x), F_18(x) + F_64(x) + F_87(x))<br />
  
    Eq(F_87(x), F_4(x)*F_88(x))<br />
  
    Eq(F_88(x), F_101(x) + F_89(x))<br />
  
    Eq(F_89(x), F_4(x) + F_90(x))<br />
  
    Eq(F_90(x), F_18(x) + F_91(x) + F_98(x))<br />
  
    Eq(F_91(x), F_4(x)*F_92(x))<br />
  
    Eq(F_92(x), F_93(x) + F_96(x))<br />
  
    Eq(F_93(x), F_4(x) + F_94(x))<br />
  
    Eq(F_94(x), F_95(x))<br />
  
    Eq(F_95(x), x**2)<br />
  
    Eq(F_96(x), F_97(x) + F_99(x))<br />
  
    Eq(F_97(x), F_98(x))<br />
  
    Eq(F_98(x), F_15(x)*F_4(x))<br />
  
    Eq(F_99(x), F_100(x))<br />
  
    Eq(F_100(x), F_26(x)*F_4(x))<br />
  
    Eq(F_101(x), F_102(x) + F_63(x))<br />
  
    Eq(F_102(x), F_103(x) + F_110(x) + 2*F_18(x))<br />
  
    Eq(F_103(x), F_104(x)*F_4(x))<br />
  
    Eq(F_104(x), F_105(x) + F_108(x))<br />
  
    Eq(F_105(x), F_106(x) + F_63(x))<br />
  
    Eq(F_106(x), F_107(x))<br />
  
    Eq(F_107(x), F_4(x)*F_86(x))<br />
  
    Eq(F_108(x), F_109(x) + F_132(x))<br />
  
    Eq(F_109(x), F_110(x))<br />
  
    Eq(F_110(x), F_111(x)*F_4(x))<br />
  
    Eq(F_111(x), F_112(x) + F_130(x) + F_18(x))<br />
  
    Eq(F_112(x), F_113(x)*F_4(x))<br />
  
    Eq(F_113(x), F_114(x) + F_122(x))<br />
  
    Eq(F_114(x), F_115(x) + F_15(x))<br />
  
    Eq(F_115(x), F_116(x) + F_18(x) + F_91(x))<br />
  
    Eq(F_116(x), F_117(x)*F_4(x))<br />
  
    Eq(F_117(x), F_118(x) + F_15(x))<br />
  
    Eq(F_118(x), F_119(x) + F_18(x) + F_98(x))<br />
  
    Eq(F_119(x), F_120(x)*F_4(x))<br />
  
    Eq(F_120(x), F_121(x) + F_4(x))<br />
  
    Eq(F_121(x), F_95(x))<br />
  
    Eq(F_122(x), F_123(x) + F_66(x))<br />
  
    Eq(F_123(x), F_103(x) + F_124(x) + 2*F_18(x))<br />
  
    Eq(F_124(x), F_125(x)*F_4(x))<br />
  
    Eq(F_125(x), F_111(x) + F_126(x))<br />
  
    Eq(F_126(x), F_110(x) + F_127(x) + 2*F_18(x))<br />
  
    Eq(F_127(x), F_128(x)*F_4(x))<br />
  
    Eq(F_128(x), F_129(x) + F_63(x))<br />
  
    Eq(F_129(x), F_107(x))<br />
  
    Eq(F_130(x), F_131(x)*F_4(x))<br />
  
    Eq(F_131(x), F_2(x) + F_86(x))<br />
  
    Eq(F_132(x), F_133(x))<br />
  
    Eq(F_133(x), F_134(x)*F_4(x))<br />
  
    Eq(F_134(x), F_135(x) + F_145(x) + 2*F_18(x))<br />
  
    Eq(F_135(x), F_136(x)*F_4(x))<br />
  
    Eq(F_136(x), F_137(x) + F_141(x))<br />
  
    Eq(F_137(x), F_138(x) + F_26(x))<br />
  
    Eq(F_138(x), F_139(x))<br />
  
    Eq(F_139(x), F_140(x)*F_4(x))<br />
  
    Eq(F_140(x), F_97(x))<br />
  
    Eq(F_141(x), F_142(x) + F_76(x))<br />
  
    Eq(F_142(x), F_143(x))<br />
  
    Eq(F_143(x), F_144(x)*F_4(x))<br />
  
    Eq(F_144(x), F_109(x))<br />
  
    Eq(F_145(x), F_146(x)*F_4(x))<br />
  
    Eq(F_146(x), F_63(x))<br />
  
    Eq(F_147(x), F_148(x) + F_151(x))<br />
  
    Eq(F_148(x), F_149(x))<br />
  
    Eq(F_149(x), F_150(x)*F_4(x))<br />
  
    Eq(F_150(x), F_111(x))<br />
  
    Eq(F_151(x), F_152(x))<br />
  
    Eq(F_152(x), F_153(x)*F_4(x))<br />
  
    Eq(F_153(x), F_134(x))<br />
  
    Eq(F_154(x), F_155(x)*F_4(x))<br />
  
    Eq(F_155(x), F_156(x) + F_164(x))<br />
  
    Eq(F_156(x), F_111(x) + F_157(x))<br />
  
    Eq(F_157(x), F_158(x) + F_161(x) + 2*F_18(x))<br />
  
    Eq(F_158(x), F_159(x)*F_4(x))<br />
  
    Eq(F_159(x), F_160(x) + F_60(x))<br />
  
    Eq(F_160(x), F_84(x))<br />
  
    Eq(F_161(x), F_162(x)*F_4(x))<br />
  
    Eq(F_162(x), F_111(x) + F_163(x))<br />
  
    Eq(F_163(x), F_145(x))<br />
  
    Eq(F_164(x), F_165(x) + F_166(x))<br />
  
    Eq(F_165(x), F_145(x))<br />
  
    Eq(F_166(x), F_167(x) + F_169(x) + 3*F_18(x))<br />
  
    Eq(F_167(x), F_168(x)*F_4(x))<br />
  
    Eq(F_168(x), F_71(x))<br />
  
    Eq(F_169(x), F_170(x)*F_4(x))<br />
  
    Eq(F_170(x), F_165(x))<br />
  
    Eq(F_171(x), F_172(x)*F_4(x))<br />
  
    Eq(F_172(x), F_173(x) + F_182(x))<br />
  
    Eq(F_173(x), F_174(x) + F_2(x))<br />
  
    Eq(F_174(x), F_175(x) + F_18(x) + F_181(x))<br />
  
    Eq(F_175(x), F_176(x)*F_4(x))<br />
  
    Eq(F_176(x), F_177(x) + F_179(x))<br />
  
    Eq(F_177(x), F_11(x) + F_178(x))<br />
  
    Eq(F_178(x), F_18(x) + F_24(x) + F_35(x))<br />
  
    Eq(F_179(x), F_180(x) + F_60(x))<br />
  
    Eq(F_180(x), F_161(x) + 2*F_18(x) + F_80(x))<br />
  
    Eq(F_181(x), F_131(x)*F_4(x))<br />
  
    Eq(F_182(x), F_111(x) + F_183(x))<br />
  
    Eq(F_183(x), F_158(x) + F_18(x) + F_184(x) + F_202(x))<br />
  
    Eq(F_184(x), F_185(x)*F_4(x))<br />
  
    Eq(F_185(x), F_186(x) + F_193(x))<br />
  
    Eq(F_186(x), F_17(x) + F_187(x))<br />
  
    Eq(F_187(x), F_18(x) + F_188(x) + F_190(x) + F_53(x))<br />
  
    Eq(F_188(x), F_189(x)*F_4(x))<br />
  
    Eq(F_189(x), F_21(x))<br />
  
    Eq(F_190(x), F_191(x)*F_4(x))<br />
  
    Eq(F_191(x), F_192(x) + F_40(x))<br />
  
    Eq(F_192(x), F_44(x))<br />
  
    Eq(F_193(x), F_194(x) + F_68(x))<br />
  
    Eq(F_194(x), F_169(x) + 2*F_18(x) + F_195(x) + F_197(x))<br />
  
    Eq(F_195(x), F_196(x)*F_4(x))<br />
  
    Eq(F_196(x), F_71(x))<br />
  
    Eq(F_197(x), F_198(x)*F_4(x))<br />
  
    Eq(F_198(x), F_148(x) + F_199(x))<br />
  
    Eq(F_199(x), F_200(x))<br />
  
    Eq(F_200(x), F_201(x)*F_4(x))<br />
  
    Eq(F_201(x), F_163(x))<br />
  
    Eq(F_202(x), F_203(x)*F_4(x))<br />
  
    Eq(F_203(x), F_111(x) + F_134(x))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;extra_basis&#34;: [], &#34;ignore_parent&#34;: false, &#34;maxreqlen&#34;: 1, &#34;one_cell_only&#34;: false, &#34;strategy_class&#34;: &#34;CellInsertionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;point_only&#34;: false, &#34;strategy_class&#34;: &#34;PatternPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;point_placements&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 0], [1, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: 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{&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 0], [1, 2]]}], 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{&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 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[[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, 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{&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], 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[[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], 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&#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 3]], [[1, 0], [1, 1], [1, 2], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], 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[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], 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{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], 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2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], 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{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 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{&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 0], [1, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: 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1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 3]], [[1, 0], [1, 1], [1, 2]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 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2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: 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1], [0, 1], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 3]], [[1, 0], [1, 1], [1, 2]]], 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[0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 3]], [[1, 0], [1, 1], [1, 2]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, 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0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 3]], [[1, 0], [1, 1], [1, 2]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], 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0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], 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{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}], [{&#34;patt&#34;: 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2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], 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&#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: 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0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 4]], [[1, 0], [1, 1], [1, 2], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 0], [1, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: 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0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], 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{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: 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[0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], 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[{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 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[[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 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&#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: 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0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 2], [1, 4]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], 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[0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, 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[{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 2], [1, 4]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 0], [1, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: 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{&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: 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3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 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[0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], 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[[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 5]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 5]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 5]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 5], [1, 5]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 4], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 5], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 5], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 5], [1, 4]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 5], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 5]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: 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&#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 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&#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: 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&#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, &#34;rule_class&#34;: &#34;EquivalenceRule&#34;}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;original_rule&#34;: {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, &#34;rule_class&#34;: &#34;EquivalenceRule&#34;}]}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;rule_class&#34;: &#34;EquivalencePathRule&#34;, &#34;rules&#34;: [{&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;original_rule&#34;: {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 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