0123_0231_0312_1032_1302<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 57, 169, 503, 1501, 4480, 13368, 39886, 119009, 355095, 1059522, 3161367, 9432779, 28145205, 83978710, 250572835, 747650748, 2230815003, 6656230320, 19860634802, 59259490102, 176816461412, 527578974643, 1574172292910, 4696962022502, 14014636352195, 41816397736090, 124770352628443, 372285556333087, 1110813046004344, 3314406380218162, 9889413608118443, 29507697696985713, 88044069939790479, 262702916749570049, 783844073949857257, 2338807425012401826, 6978454456801902710, 20822076279067784828, 62128206647351163901, 185376040769589367165, 553118757901143765714, 1650377034011469183189, 4924339150471001986567, 14693076532894211346753, 43840704590957655623146, 130810410925765639299559, 390307677903903099562722, 1164586842534951805935523, 3474854814768597532043128, 10368154218055334547495440, 30936147729826037840316258, 92306230813484702667849934, 275420208146265711146685501, 821789497705833549904247914, 2452027696460670128486304014, 7316277271728317409927964645, 21830060563374605072811536332, 65135796047820895325846513289, 194349984255264279692019553849, 579894906823436682554640467222, 1730270801144423980018095228714, 5162723469486367423857066171183, 15404359597790262927693958658253, 45963006932393589675709836080573, 137142864840048972581080067735607, 409202239622847896424544707366181, 1220963796458890096977131000592832, 3643070462266525457025891417455172, 10870070375166691539792965953467330, 32433748176137285649418611078091521, 96774720351059104913155710043496099, 288753136028728461577350162721427470, 861571836776822758148007752528544875, 2570728893670387809482304523405490587, 7670453887484308304419818960593973737, 22886840765235091149280925296296071126, 68288981055985566346313988750303433847, 203758350988678002943243702945282827220, 607967273132804632026079328145400296283, 1814032177856978907065864648090786204056, 5412647831097496017839591463321096041626, 16150075451304496772826831256607136805282, 48188048663410261738203309414471238839572, 143781869068582743282998607693274295965755, 429011475796746437590595822236942852716522, 1280069925071788066427159194954766847480158, 3819429328854610248422422482694511730146527, 11396283993858117779014637308255336849975470, 34003846566160811578367338279414326725790491, 101459526799977859505087475510482551840983143, 302731502991770756977497301654084144163216860, 903280015136799414376318896929954837736159814, 2695176344986190090331534170326675092964745775, 8041775981806714163174985660269719126678203933, 23994779065892516674997675175051558096221328931, 71594809868310009561307863268453297012903520457<br /><br />


Generating function in Maple syntax:<br />
-(x^3-2*x^2+3*x-1)/(x^5-3*x^3+4*x^2-4*x+1)<br /><br />



Generating function in latex syntax:<br />
-\frac{x^{3}-2 x^{2}+3 x -1}{x^{5}-3 x^{3}+4 x^{2}-4 x +1}<br /><br />



Generating function in sympy syntax:<br />
(-x**3 + 2*x**2 - 3*x + 1)/(x**5 - 3*x**3 + 4*x**2 - 4*x + 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^5-3*x^3+4*x^2-4*x+1)*F(x)+x^3-2*x^2+3*x-1 = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{5}-3 x^{3}+4 x^{2}-4 x +1\right) F \! \left(x \right)+x^{3}-2 x^{2}+3 x -1 = 0<br /><br />



Explicit closed form in Maple syntax:<br />
103916/2758245361*((((RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-917/1252)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-917/1252*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+189/626)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-917/1252*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+189/626)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+189/626*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+323/626)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+((-917/1252*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+189/626)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+189/626*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+323/626)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(189/626*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+323/626)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+323/626*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-10289/1252)*((((-1-84/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(8906/1411+1984/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-6097/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((-1-84/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(18834/1411+573/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(101315/1411+7884/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-81669/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((8906/1411+1984/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(101315/1411+7884/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-12230/1411-83887/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-44386/1411+69439/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-6097/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(-6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-81669/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-44386/1411+69439/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-107647/1411-44386/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^(-n+1)+(((1022/1411+84/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-1984/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(63/1411-70/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-1984/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+63/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+694/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((63/1411-70/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-1984/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(152496/1411-191110/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-70/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-74042/1411+152496/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+63/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+63/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+694/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-74042/1411+152496/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+63/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-107647/1411-74042/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+694/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)^(-n+1)+(((84/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+1)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-584/83+RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^4+((-584/83+RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-6677/83-584/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((-252/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-3)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+1752/83-3*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-71838/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+96157/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+277850/1411+96157/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-62677/1411+66373/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-352654/1411-62677/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^(-n+1)+(((-1-84/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(8906/1411+1984/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-6097/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((8906/1411+1984/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(70/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+107349/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-82363/1411-63/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-6097/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-82363/1411-63/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+29656/1411-694/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^(-n+2)+(((84/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+1)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-584/83+RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((-584/83+RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-6677/83-584/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-7814/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+6034/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-694/1411+6034/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-694/1411+6034/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+29656/1411-694/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^(-n+2)+(((84/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+1)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-584/83+RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-1984/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-8906/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-107412/1411-8906/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(6097/1411+1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+81669/1411+6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^(-n+3)+(((-73317/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+60729/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-22965/1411+60729/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-22965/1411+60729/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+101382/1411-22965/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n+1)+(((-3530/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+10267/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-30478/1411+10267/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-30478/1411+10267/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-310871/1411-30478/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n+2)+(((-3395/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+1022/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+6097/1411+1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(6097/1411+1022/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+81669/1411+6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n+3)+(((-84/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-1)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+584/83-RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(584/83-RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+6677/83+584/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n+4)+(((6097/1411+RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-8906/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(82363/1411-107349/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-8906/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+82363/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-29656/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((82363/1411-107349/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-8906/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-60725/1411+222977/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-107349/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-55603/1411-60725/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+82363/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+82363/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-29656/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-55603/1411-60725/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+82363/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-902249/1411-55603/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-29656/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)^(-n)+(((584/83-RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(107412/1411+8906/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-81669/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^3-((RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-584/83)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-107412/1411-8906/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+81669/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((107412/1411+8906/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(-6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-81669/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-404236/1411+58251/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+214485/1411-31069/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-6097/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-81669/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(214485/1411-31069/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-1004763/1411-55603/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^(-n)+(((-584/83+RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-6677/83-584/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^4+((-3*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+1752/83)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+20031/83+1752/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((84969/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-82000/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-522859/1411-82000/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-30522/1411-49360/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-652677/1411-30522/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^(-n)+(((79325/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-42288/1411)*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-68823/1411-42288/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-68823/1411-42288/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-1116641/1411-68823/1411*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n)-52519/83*RootOf(_Z^5-3*_Z^3+4*_Z^2-4*_Z+1,index = 5)^(-n))<br /><br />



Explicit closed form in latex syntax:<br />
\frac{103916 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{917}{1252}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{917 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1252}+\frac{189}{626}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{917 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1252}+\frac{189}{626}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{189 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{626}+\frac{323}{626}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(-\frac{917 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1252}+\frac{189}{626}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{189 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{626}+\frac{323}{626}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{189 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{626}+\frac{323}{626}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{323 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{626}-\frac{10289}{1252}\right) \left(\left(\left(\left(-1-\frac{84 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{8906}{1411}+\frac{1984 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{6097}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-1-\frac{84 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{18834}{1411}+\frac{573 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{101315}{1411}+\frac{7884 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{81669}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{8906}{1411}+\frac{1984 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{101315}{1411}+\frac{7884 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{12230}{1411}-\frac{83887 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{44386}{1411}+\frac{69439 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{6097}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{81669}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{44386}{1411}+\frac{69439 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{107647}{1411}-\frac{44386 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(\frac{1022}{1411}+\frac{84 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{83}-\frac{1984 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{63}{1411}-\frac{70 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{1984 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}+\frac{63 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{694}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{63}{1411}-\frac{70 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{1984 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{152496}{1411}-\frac{191110 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{70 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{74042}{1411}+\frac{152496 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{63 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}+\frac{63 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{694}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{74042}{1411}+\frac{152496 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{63 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{107647}{1411}-\frac{74042 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{694 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(\frac{84 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{584}{83}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{584}{83}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{6677}{83}-\frac{584 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{252 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}-3\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1752}{83}-3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{71838 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{96157}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{277850}{1411}+\frac{96157 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{62677}{1411}+\frac{66373 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{352654}{1411}-\frac{62677 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-1-\frac{84 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{8906}{1411}+\frac{1984 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{6097}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{8906}{1411}+\frac{1984 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{70 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}+\frac{107349}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{82363}{1411}-\frac{63 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{6097}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{82363}{1411}-\frac{63 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{29656}{1411}-\frac{694 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(\frac{84 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{584}{83}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{584}{83}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{6677}{83}-\frac{584 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{7814 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{6034}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{694}{1411}+\frac{6034 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{694}{1411}+\frac{6034 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{29656}{1411}-\frac{694 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(\frac{84 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{584}{83}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1984 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{8906}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{107412}{1411}-\frac{8906 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{6097}{1411}+\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{81669}{1411}+\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{73317 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{60729}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{22965}{1411}+\frac{60729 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{22965}{1411}+\frac{60729 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{101382}{1411}-\frac{22965 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{3530 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{10267}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{30478}{1411}+\frac{10267 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{30478}{1411}+\frac{10267 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{310871}{1411}-\frac{30478 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{3395 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{1022}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{6097}{1411}+\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{6097}{1411}+\frac{1022 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{81669}{1411}+\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-\frac{84 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{584}{83}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{584}{83}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{6677}{83}+\frac{584 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(\frac{6097}{1411}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}-\frac{8906 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{82363}{1411}-\frac{107349 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{8906 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}+\frac{82363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{29656}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{82363}{1411}-\frac{107349 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{8906 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{60725}{1411}+\frac{222977 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{107349 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{55603}{1411}-\frac{60725 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{82363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}+\frac{82363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{29656}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{55603}{1411}-\frac{60725 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}+\frac{82363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{902249}{1411}-\frac{55603 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{29656 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\frac{584}{83}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{107412}{1411}+\frac{8906 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{81669}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{584}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{107412}{1411}-\frac{8906 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}+\frac{81669}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{107412}{1411}+\frac{8906 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{81669}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{404236}{1411}+\frac{58251 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{214485}{1411}-\frac{31069 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{6097 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}-\frac{81669}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{214485}{1411}-\frac{31069 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1004763}{1411}-\frac{55603 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(-\frac{584}{83}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{6677}{83}-\frac{584 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{1752}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{20031}{83}+\frac{1752 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{83}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{84969 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{82000}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{522859}{1411}-\frac{82000 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{30522}{1411}-\frac{49360 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{652677}{1411}-\frac{30522 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{79325 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}-\frac{42288}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{68823}{1411}-\frac{42288 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{68823}{1411}-\frac{42288 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1116641}{1411}-\frac{68823 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{1411}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}-\frac{52519 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{83}\right)}{2758245361}<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) = 19<br />
    
    a(n) = 3*a(n+2)-4*a(n+3)+4*a(n+4)-a(n+5), n >= 5<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) = 19<br />
    
    a \! \left(n \right) = 3 a \! \left(n +2\right)-4 a \! \left(n +3\right)+4 a \! \left(n +4\right)-a \! \left(n +5\right), \quad n \geq 5<br /><br />
  



  Specification 1<br />
  Strategy pack name: point_placements<br />
  Tree: http://permpal.com/tree/17005/<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[18,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[13,x]<br />
  
    F[10,x] = F[1,x]+F[11,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[10,x]*F[4,x]<br />
  
    F[13,x] = F[11,x]+F[14,x]<br />
  
    F[14,x] = F[15,x]<br />
  
    F[15,x] = F[16,x]*F[4,x]<br />
  
    F[16,x] = F[17,x]+F[4,x]<br />
  
    F[17,x] = F[15,x]<br />
  
    F[18,x] = F[19,x]+F[2,x]<br />
  
    F[19,x] = F[20,x]+F[21,x]+F[87,x]<br />
  
    F[20,x] = 0<br />
  
    F[21,x] = F[22,x]*F[4,x]<br />
  
    F[22,x] = F[23,x]+F[36,x]<br />
  
    F[23,x] = F[24,x]+F[27,x]<br />
  
    F[24,x] = F[25,x]<br />
  
    F[25,x] = F[26,x]*F[4,x]<br />
  
    F[26,x] = F[1,x]+F[4,x]<br />
  
    F[27,x] = F[20,x]+F[28,x]+F[34,x]<br />
  
    F[28,x] = F[29,x]*F[4,x]<br />
  
    F[29,x] = F[30,x]+F[33,x]<br />
  
    F[30,x] = F[31,x]+F[4,x]<br />
  
    F[31,x] = F[32,x]<br />
  
    F[32,x] = F[11,x]*F[4,x]<br />
  
    F[33,x] = F[17,x]<br />
  
    F[34,x] = F[35,x]*F[4,x]<br />
  
    F[35,x] = F[11,x]+F[17,x]<br />
  
    F[36,x] = F[37,x]+F[76,x]<br />
  
    F[37,x] = F[20,x]+F[21,x]+F[38,x]<br />
  
    F[38,x] = F[39,x]*F[4,x]<br />
  
    F[39,x] = F[2,x]+F[40,x]<br />
  
    F[40,x] = F[20,x]+F[41,x]+F[75,x]<br />
  
    F[41,x] = F[4,x]*F[42,x]<br />
  
    F[42,x] = F[43,x]+F[45,x]<br />
  
    F[43,x] = F[4,x]+F[44,x]<br />
  
    F[44,x] = F[20,x]+F[28,x]+F[32,x]<br />
  
    F[45,x] = F[40,x]+F[46,x]<br />
  
    F[46,x] = F[20,x]+F[47,x]+F[66,x]+F[70,x]<br />
  
    F[47,x] = F[4,x]*F[48,x]<br />
  
    F[48,x] = F[49,x]+F[56,x]<br />
  
    F[49,x] = F[50,x]+F[53,x]<br />
  
    F[50,x] = F[51,x]<br />
  
    F[51,x] = F[4,x]*F[52,x]<br />
  
    F[52,x] = F[4,x]<br />
  
    F[53,x] = F[54,x]<br />
  
    F[54,x] = F[4,x]*F[55,x]<br />
  
    F[55,x] = F[17,x]<br />
  
    F[56,x] = F[57,x]+F[60,x]<br />
  
    F[57,x] = 2*F[20,x]+F[47,x]+F[58,x]<br />
  
    F[58,x] = F[4,x]*F[59,x]<br />
  
    F[59,x] = F[40,x]<br />
  
    F[60,x] = F[61,x]<br />
  
    F[61,x] = F[4,x]*F[62,x]<br />
  
    F[62,x] = F[63,x]<br />
  
    F[63,x] = F[64,x]<br />
  
    F[64,x] = F[4,x]*F[65,x]<br />
  
    F[65,x] = F[40,x]+F[63,x]<br />
  
    F[66,x] = F[4,x]*F[67,x]<br />
  
    F[67,x] = F[68,x]+F[74,x]<br />
  
    F[68,x] = F[40,x]+F[69,x]<br />
  
    F[69,x] = F[70,x]<br />
  
    F[70,x] = F[4,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[2,x]+F[71,x]<br />
  
    F[74,x] = F[63,x]<br />
  
    F[75,x] = F[2,x]*F[4,x]<br />
  
    F[76,x] = F[20,x]+F[66,x]+F[77,x]+F[85,x]<br />
  
    F[77,x] = F[4,x]*F[78,x]<br />
  
    F[78,x] = F[79,x]+F[82,x]<br />
  
    F[79,x] = F[80,x]+F[81,x]<br />
  
    F[80,x] = F[51,x]<br />
  
    F[81,x] = F[54,x]<br />
  
    F[82,x] = F[83,x]+F[84,x]<br />
  
    F[83,x] = 2*F[20,x]+F[58,x]+F[77,x]<br />
  
    F[84,x] = F[61,x]<br />
  
    F[85,x] = F[4,x]*F[86,x]<br />
  
    F[86,x] = F[63,x]+F[71,x]<br />
  
    F[87,x] = F[4,x]*F[88,x]<br />
  
    F[88,x] = F[89,x]+F[91,x]<br />
  
    F[89,x] = F[2,x]+F[90,x]<br />
  
    F[90,x] = F[20,x]+F[41,x]+F[72,x]<br />
  
    F[91,x] = F[71,x]+F[92,x]<br />
  
    F[92,x] = F[64,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_{18}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{17}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{87}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = 0<br />
  
    F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{36}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{25}\! \left(x \right)<br />
  
    F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)+F_{34}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{32}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{17}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{76}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{38}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{2}\! \left(x \right)+F_{40}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)+F_{75}\! \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_{43}\! \left(x \right)+F_{45}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{4}\! \left(x \right)+F_{44}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)+F_{32}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{56}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = F_{51}\! \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_{4}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{54}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{17}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{60}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{47}\! \left(x \right)+F_{58}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)<br />
  
    F_{59}\! \left(x \right) = F_{40}\! \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_{63}\! \left(x \right)<br />
  
    F_{63}\! \left(x \right) = F_{64}\! \left(x \right)<br />
  
    F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)<br />
  
    F_{65}\! \left(x \right) = F_{40}\! \left(x \right)+F_{63}\! \left(x \right)<br />
  
    F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)<br />
  
    F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{74}\! \left(x \right)<br />
  
    F_{68}\! \left(x \right) = F_{40}\! \left(x \right)+F_{69}\! \left(x \right)<br />
  
    F_{69}\! \left(x \right) = F_{70}\! \left(x \right)<br />
  
    F_{70}\! \left(x \right) = F_{4}\! \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_{2}\! \left(x \right)+F_{71}\! \left(x \right)<br />
  
    F_{74}\! \left(x \right) = F_{63}\! \left(x \right)<br />
  
    F_{75}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{76}\! \left(x \right) = F_{20}\! \left(x \right)+F_{66}\! \left(x \right)+F_{77}\! \left(x \right)+F_{85}\! \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_{79}\! \left(x \right)+F_{82}\! \left(x \right)<br />
  
    F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)<br />
  
    F_{80}\! \left(x \right) = F_{51}\! \left(x \right)<br />
  
    F_{81}\! \left(x \right) = F_{54}\! \left(x \right)<br />
  
    F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)<br />
  
    F_{83}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{58}\! \left(x \right)+F_{77}\! \left(x \right)<br />
  
    F_{84}\! \left(x \right) = F_{61}\! \left(x \right)<br />
  
    F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)<br />
  
    F_{86}\! \left(x \right) = F_{63}\! \left(x \right)+F_{71}\! \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_{89}\! \left(x \right)+F_{91}\! \left(x \right)<br />
  
    F_{89}\! \left(x \right) = F_{2}\! \left(x \right)+F_{90}\! \left(x \right)<br />
  
    F_{90}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)+F_{72}\! \left(x \right)<br />
  
    F_{91}\! \left(x \right) = F_{71}\! \left(x \right)+F_{92}\! \left(x \right)<br />
  
    F_{92}\! \left(x \right) = F_{64}\! \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_18(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_13(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_10(x)*F_4(x))<br />
  
    Eq(F_13(x), F_11(x) + F_14(x))<br />
  
    Eq(F_14(x), F_15(x))<br />
  
    Eq(F_15(x), F_16(x)*F_4(x))<br />
  
    Eq(F_16(x), F_17(x) + F_4(x))<br />
  
    Eq(F_17(x), F_15(x))<br />
  
    Eq(F_18(x), F_19(x) + F_2(x))<br />
  
    Eq(F_19(x), F_20(x) + F_21(x) + F_87(x))<br />
  
    Eq(F_20(x), 0)<br />
  
    Eq(F_21(x), F_22(x)*F_4(x))<br />
  
    Eq(F_22(x), F_23(x) + F_36(x))<br />
  
    Eq(F_23(x), F_24(x) + F_27(x))<br />
  
    Eq(F_24(x), F_25(x))<br />
  
    Eq(F_25(x), F_26(x)*F_4(x))<br />
  
    Eq(F_26(x), F_1(x) + F_4(x))<br />
  
    Eq(F_27(x), F_20(x) + F_28(x) + F_34(x))<br />
  
    Eq(F_28(x), F_29(x)*F_4(x))<br />
  
    Eq(F_29(x), F_30(x) + F_33(x))<br />
  
    Eq(F_30(x), F_31(x) + F_4(x))<br />
  
    Eq(F_31(x), F_32(x))<br />
  
    Eq(F_32(x), F_11(x)*F_4(x))<br />
  
    Eq(F_33(x), F_17(x))<br />
  
    Eq(F_34(x), F_35(x)*F_4(x))<br />
  
    Eq(F_35(x), F_11(x) + F_17(x))<br />
  
    Eq(F_36(x), F_37(x) + F_76(x))<br />
  
    Eq(F_37(x), F_20(x) + F_21(x) + F_38(x))<br />
  
    Eq(F_38(x), F_39(x)*F_4(x))<br />
  
    Eq(F_39(x), F_2(x) + F_40(x))<br />
  
    Eq(F_40(x), F_20(x) + F_41(x) + F_75(x))<br />
  
    Eq(F_41(x), F_4(x)*F_42(x))<br />
  
    Eq(F_42(x), F_43(x) + F_45(x))<br />
  
    Eq(F_43(x), F_4(x) + F_44(x))<br />
  
    Eq(F_44(x), F_20(x) + F_28(x) + F_32(x))<br />
  
    Eq(F_45(x), F_40(x) + F_46(x))<br />
  
    Eq(F_46(x), F_20(x) + F_47(x) + F_66(x) + F_70(x))<br />
  
    Eq(F_47(x), F_4(x)*F_48(x))<br />
  
    Eq(F_48(x), F_49(x) + F_56(x))<br />
  
    Eq(F_49(x), F_50(x) + F_53(x))<br />
  
    Eq(F_50(x), F_51(x))<br />
  
    Eq(F_51(x), F_4(x)*F_52(x))<br />
  
    Eq(F_52(x), F_4(x))<br />
  
    Eq(F_53(x), F_54(x))<br />
  
    Eq(F_54(x), F_4(x)*F_55(x))<br />
  
    Eq(F_55(x), F_17(x))<br />
  
    Eq(F_56(x), F_57(x) + F_60(x))<br />
  
    Eq(F_57(x), 2*F_20(x) + F_47(x) + F_58(x))<br />
  
    Eq(F_58(x), F_4(x)*F_59(x))<br />
  
    Eq(F_59(x), F_40(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_63(x))<br />
  
    Eq(F_63(x), F_64(x))<br />
  
    Eq(F_64(x), F_4(x)*F_65(x))<br />
  
    Eq(F_65(x), F_40(x) + F_63(x))<br />
  
    Eq(F_66(x), F_4(x)*F_67(x))<br />
  
    Eq(F_67(x), F_68(x) + F_74(x))<br />
  
    Eq(F_68(x), F_40(x) + F_69(x))<br />
  
    Eq(F_69(x), F_70(x))<br />
  
    Eq(F_70(x), F_4(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_2(x) + F_71(x))<br />
  
    Eq(F_74(x), F_63(x))<br />
  
    Eq(F_75(x), F_2(x)*F_4(x))<br />
  
    Eq(F_76(x), F_20(x) + F_66(x) + F_77(x) + F_85(x))<br />
  
    Eq(F_77(x), F_4(x)*F_78(x))<br />
  
    Eq(F_78(x), F_79(x) + F_82(x))<br />
  
    Eq(F_79(x), F_80(x) + F_81(x))<br />
  
    Eq(F_80(x), F_51(x))<br />
  
    Eq(F_81(x), F_54(x))<br />
  
    Eq(F_82(x), F_83(x) + F_84(x))<br />
  
    Eq(F_83(x), 2*F_20(x) + F_58(x) + F_77(x))<br />
  
    Eq(F_84(x), F_61(x))<br />
  
    Eq(F_85(x), F_4(x)*F_86(x))<br />
  
    Eq(F_86(x), F_63(x) + F_71(x))<br />
  
    Eq(F_87(x), F_4(x)*F_88(x))<br />
  
    Eq(F_88(x), F_89(x) + F_91(x))<br />
  
    Eq(F_89(x), F_2(x) + F_90(x))<br />
  
    Eq(F_90(x), F_20(x) + F_41(x) + F_72(x))<br />
  
    Eq(F_91(x), F_71(x) + F_92(x))<br />
  
    Eq(F_92(x), F_64(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, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#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, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#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, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#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;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#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, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}], &#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, 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0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [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;, 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[0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [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], &#34;pos&#34;: 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0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#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;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [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, 3]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [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;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#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, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [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;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#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, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#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, 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, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}], &#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;: [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;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#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, 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{&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#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]]], 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{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#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, 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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#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, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [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, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [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;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;: [[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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[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, 3]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [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;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;: [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, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#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, 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, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [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;, &#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;: [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, 1], [0, 3], [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;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#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, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#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, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 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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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#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, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: 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0, 1], &#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, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#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, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 3], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 3], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], 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[0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], 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[[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0], [0, 0]]}], &#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;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;: [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, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, 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[[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [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]]}]]}, 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{&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#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;: [[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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], 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{&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#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, 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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#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, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [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, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 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{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#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;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, 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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#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, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], 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[[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 5], [1, 0], [1, 0]]}], &#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;patt&#34;: [0], &#34;pos&#34;: [[1, 5]]}]]}, {&#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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#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, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 5], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 5], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 5], [1, 0], [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, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [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], &#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, 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, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 0]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [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;, &#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;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;: [], &#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;: [[0, 5]]}, {&#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, 5], [1, 5]]}, {&#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;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 5]]}, {&#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, 2], [1, 5]]}, {&#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, 2], [1, 3], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 4], [1, 5]]}, {&#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;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 5], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 5], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 5], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 4], [1, 5], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 5], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 5], [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, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 5], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 5], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 5], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 5], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 5], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 5], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 5], [1, 2]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 5], [1, 0], [1, 0]]}], &#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;patt&#34;: [0], &#34;pos&#34;: [[1, 5]]}]]}, {&#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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#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, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 5], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 5], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 5], [1, 0], [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, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 5], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 5], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 5], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 5], [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;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, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#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, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#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, 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, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [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;: [], 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[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;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#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, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#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, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 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[{&#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, 3]]}, {&#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, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, &#34;rule_class&#34;: &#34;EquivalenceRule&#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;requirements&#34;: []}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#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, 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;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#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;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.strategy&#34;, &#34;strategy_class&#34;: &#34;EmptyStrategy&#34;}}]}<br /><br />