0231_0312_1032_1203
Counting sequence:
1, 1, 2, 6, 20, 64, 198, 604, 1836, 5580, 16964, 51580, 156832, 476840, 1449768, 4407760, 13400920, 40742736, 123869760, 376599872, 1144972112, 3481044496, 10583375360, 32176500064, 97825797056, 297418501952, 904237607968, 2749141844096, 8358180194240, 25411266517952, 77257542997952, 234885102810560, 714118121990784, 2171124034773120, 6600840153823104, 20068448433952000, 61013842655963264, 185499591953058816, 563971995809121280, 1714636720802104320, 5212987712453928192, 15848978713971485952, 48185443766878460416, 146497577724929761792, 445394679420239840256, 1354127648638215675904, 4116936671074013697536, 12516668994004276032512, 38054265883229309379584, 115695889425947769830400, 351748707257553208005632, 1069417017936082524404736, 3251334645030867177840640, 9884990416909390695823360, 30053207747079761329227776, 91370376479487279939072000, 277792166755126551237441536, 844567910123829045700734976, 2567728828148350154695729152, 7806632546502283809603371008, 23734403356002563795925798912, 72159397705713567413395279872, 219385277950729118624502874112, 666994206046536272816933675008, 2027853806122594192330462019584, 6165257541560988804005954600960, 18744152285047279872163723812864, 56987602304783224725332634763264, 173258665799403616995795877445632, 526756067294128637999748052402176, 1601489617566544133949924775870464, 4868988046684096308465538083700736, 14803121006038960939949354691362816, 45005736185502986767617831042777088, 136830354137670006867070765140770816, 416003545331872528505673239525785600, 1264770166088778841808538780343107584, 3845264279543818882038727087688646656, 11690706956869946488317252364905349120, 35543104248642555692778688931266297856, 108061237382012862376623952045882277888, 328537173985800775381877437013088075776, 998847295344248329958852127935416107008, 3036782435644984294574631161321919217664, 9232690126335622725621530520883105628160, 28070027660980780842905127690671823519744, 85340939867646957085037252376755857391616, 259460949075490134402510320602789647745024, 788835747527023915783273848637975783276544, 2398287059358098645582838451938827642339328, 7291480941521950752266962973870297570344960, 22168194634218485741465359760376520536489984, 67397673707423463777045419056722297936150528, 204908270435368216164625602353364910031241216, 622979948463552490282162580191668839893172224, 1894037831479650112500457798008363462131974144, 5758418574985669054226030291649606157440909312, 17507245068508154518288971932893789382058704896, 53227049388219558171132469712561029524532232192, 161825505697189780144022217240736701532847734784, 491995979396654889659980410043309809484140904448
Generating function in Maple syntax:
-(x-1)*(2*x-1)^2/(2*x^5+2*x^4-10*x^3+12*x^2-6*x+1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(2 x -1\right)^{2}}{2 x^{5}+2 x^{4}-10 x^{3}+12 x^{2}-6 x +1}
Generating function in sympy syntax:
(1 - x)*(2*x - 1)**2/(2*x**5 + 2*x**4 - 10*x**3 + 12*x**2 - 6*x + 1)
Implicit equation for the generating function in Maple syntax:
(2*x^5+2*x^4-10*x^3+12*x^2-6*x+1)*F(x)+(x-1)*(2*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{5}+2 x^{4}-10 x^{3}+12 x^{2}-6 x +1\right) F \! \left(x \right)+\left(x -1\right) \left(2 x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-974/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n+3)-974/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+3)-974/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+3)-974/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n+3)-974/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n+3)-60/71*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n+2)-60/71*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+2)-60/71*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+2)-60/71*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n+2)-60/71*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n+2)+3565/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n+1)+3565/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+1)+3565/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+1)+3565/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n+1)+3565/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n+1)+673/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n-1)+673/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n-1)+673/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n-1)+673/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n-1)+673/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n-1)-2478/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n)-2478/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n)-2478/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n)-2478/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n)-2478/2059*RootOf(2*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n)
Explicit closed form in latex syntax:
-\frac{974 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{2059}-\frac{974 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{2059}-\frac{974 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{2059}-\frac{974 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{2059}-\frac{974 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{2059}-\frac{60 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{71}-\frac{60 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{71}-\frac{60 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{71}-\frac{60 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{71}-\frac{60 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{71}+\frac{3565 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{2059}+\frac{3565 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{2059}+\frac{3565 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{2059}+\frac{3565 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{2059}+\frac{3565 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{2059}+\frac{673 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{2059}+\frac{673 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{2059}+\frac{673 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{2059}+\frac{673 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{2059}+\frac{673 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{2059}-\frac{2478 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{2059}-\frac{2478 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{2059}-\frac{2478 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{2059}-\frac{2478 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{2059}-\frac{2478 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{2059}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n+5) = -2*a(n)-2*a(n+1)+10*a(n+2)-12*a(n+3)+6*a(n+4), n >= 5
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(n +5\right) = -2 a \! \left(n \right)-2 a \! \left(n +1\right)+10 a \! \left(n +2\right)-12 a \! \left(n +3\right)+6 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15773/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[13,x]*F[4,x]
F[4,x] = F[21,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[13,x]
F[12,x] = F[1,x]+F[10,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[15,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[50,x]
F[23,x] = 0
F[24,x] = F[13,x]*F[25,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[13,x]*F[29,x]
F[29,x] = F[10,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[23,x]+F[24,x]+F[32,x]
F[32,x] = F[13,x]*F[33,x]
F[33,x] = F[2,x]+F[31,x]
F[34,x] = F[35,x]
F[35,x] = F[13,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[23,x]+F[38,x]+F[48,x]
F[38,x] = F[13,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[13,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[10,x]*F[13,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = F[23,x]+F[38,x]+F[45,x]
F[45,x] = F[13,x]*F[2,x]
F[46,x] = F[47,x]
F[47,x] = F[13,x]*F[37,x]
F[48,x] = F[13,x]*F[49,x]
F[49,x] = F[2,x]+F[37,x]
F[50,x] = F[13,x]*F[51,x]
F[51,x] = F[21,x]+F[52,x]
F[52,x] = F[37,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[13,x]*F[55,x]
F[55,x] = F[31,x]+F[56,x]
F[56,x] = F[54,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{50}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{13}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)+F_{48}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13}\! \left(x \right) F_{37}\! \left(x \right)
F_{48}\! \left(x \right) = F_{13}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{21}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{37}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{31}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{54}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_13(x)*F_4(x))
Eq(F_4(x), F_21(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_13(x))
Eq(F_12(x), F_1(x) + F_10(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_15(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_50(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_13(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_13(x)*F_29(x))
Eq(F_29(x), F_10(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_23(x) + F_24(x) + F_32(x))
Eq(F_32(x), F_13(x)*F_33(x))
Eq(F_33(x), F_2(x) + F_31(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_13(x)*F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_23(x) + F_38(x) + F_48(x))
Eq(F_38(x), F_13(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_13(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_10(x)*F_13(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_23(x) + F_38(x) + F_45(x))
Eq(F_45(x), F_13(x)*F_2(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_13(x)*F_37(x))
Eq(F_48(x), F_13(x)*F_49(x))
Eq(F_49(x), F_2(x) + F_37(x))
Eq(F_50(x), F_13(x)*F_51(x))
Eq(F_51(x), F_21(x) + F_52(x))
Eq(F_52(x), F_37(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_13(x)*F_55(x))
Eq(F_55(x), F_31(x) + F_56(x))
Eq(F_56(x), F_54(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1], [3, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [1, 1], [3, 1]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[2, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [1, 1], [3, 1]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1], [3, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [1, 1]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [1, 1], [3, 1]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [1, 1]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[2, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}