0132_0321_1230_1320_2103

Counting sequence:
1, 1, 2, 6, 19, 50, 112, 234, 467, 904, 1718, 3226, 6011, 11146, 20604, 38014, 70051, 128992, 237418, 436862, 803715, 1478482, 2719592, 5002370, 9201075, 16923720, 31127902, 57253490, 105305963, 193688266, 356248692, 655243958, 1205182019, 2216675840, 4077103058, 7498962230, 13792742515, 25368809266, 46660515552, 85822068954, 157851395475, 290333981768, 534007448070, 982192827274, 1806534259163, 3322734536650, 6111461625324, 11240730423470, 20674926587875, 38027118639200, 69942775653178, 128644820882990, 236614715178211, 435202311717330, 800461847781592, 1472278874680306, 2707943034182515, 4980683756647816, 9160905665514158, 16849532456348130, 30991121878513867, 57001560000380042, 104842214335246052, 192834896214144102, 354678670549774467, 652355781099169024, 1199869347863092130, 2206903799512040294, 4059128928474306259, 7465902075849443634, 13731934803835795280, 25256965808159550410, 46454802687844794707, 85443703299840145928, 157155471795844496726, 289053977783529443194, 531653152879214091835, 977862602458588037898, 1798569733121331579228, 3308085488459133715422, 6084517824039053339171, 11191173045619518640608, 20583776358117705702154, 37859467227776277689054, 69634416631513502039107, 128077660217407485437778, 235571544076697265173576, 433283620925618252658274, 796932825219723003277619, 1465787990222038521117640, 2696004436367379777061886, 4958725251809141301465682, 9120517678398559599653931, 16775247366575080678190410, 30854490296782781579319124, 56750255341756421857172758, 104379993005114284114691779, 191984738643653487551193344, 353114986990524193523067762, 649479718639291965188962966, 1194579444273469646263234355

Generating function in Maple syntax:
(x^7-4*x^6-x^5+4*x^4+x^3+3*x^2-3*x+1)/(x^3+x^2+x-1)/(x-1)^3

Generating function in latex syntax:
\frac{x^{7}-4 x^{6}-x^{5}+4 x^{4}+x^{3}+3 x^{2}-3 x +1}{\left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3}}

Generating function in sympy syntax:
(x**7 - 4*x**6 - x**5 + 4*x**4 + x**3 + 3*x**2 - 3*x + 1)/((x - 1)**3*(x**3 + x**2 + x - 1))

Implicit equation for the generating function in Maple syntax:
-(x^3+x^2+x-1)*(x-1)^3*F(x)+x^7-4*x^6-x^5+4*x^4+x^3+3*x^2-3*x+1 = 0

Implicit equation for the generating function in latex syntax:
-\left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{7}-4 x^{6}-x^{5}+4 x^{4}+x^{3}+3 x^{2}-3 x +1 = 0

Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/264*(((-35*11^(1/2)+165*I)*3^(1/2)-105*I*11^(1/2)+165)*(17+3*11^(1/2)*3^(1/2))^(1/3)+396+((25*11^(1/2)+165*I)*3^(1/2)-75*I*11^(1/2)-165)*(17+3*11^(1/2)*3^(1/2))^(2/3))*(1/24*((17*I+3*11^(1/2))*3^(1/2)-9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/264*(((25*11^(1/2)-165*I)*3^(1/2)+75*I*11^(1/2)-165)*(17+3*11^(1/2)*3^(1/2))^(2/3)+396+((-35*11^(1/2)-165*I)*3^(1/2)+105*I*11^(1/2)+165)*(17+3*11^(1/2)*3^(1/2))^(1/3))*(1/24*((-17*I+3*11^(1/2))*3^(1/2)+9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/264*((-50*11^(1/2)*3^(1/2)+330)*(17+3*11^(1/2)*3^(1/2))^(2/3)+70*(17+3*11^(1/2)*3^(1/2))^(1/3)*11^(1/2)*3^(1/2)-330*(17+3*11^(1/2)*3^(1/2))^(1/3)+396)*(1/3*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3+17/12*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/4*(17+3*11^(1/2)*3^(1/2))^(2/3)*11^(1/2)*3^(1/2))^(-n)-1/2*n^2-9/2*n-3/2)

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(\left(\left(-35 \sqrt{11}+165 \,\mathrm{I}\right) \sqrt{3}-105 \,\mathrm{I} \sqrt{11}+165\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+396+\left(\left(25 \sqrt{11}+165 \,\mathrm{I}\right) \sqrt{3}-75 \,\mathrm{I} \sqrt{11}-165\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}-\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{264}\\+\\\frac{\left(\left(\left(25 \sqrt{11}-165 \,\mathrm{I}\right) \sqrt{3}+75 \,\mathrm{I} \sqrt{11}-165\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+396+\left(\left(-35 \sqrt{11}-165 \,\mathrm{I}\right) \sqrt{3}+105 \,\mathrm{I} \sqrt{11}+165\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}+\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{264}\\+\\\frac{\left(\left(-50 \sqrt{11}\, \sqrt{3}+330\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+70 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{11}\, \sqrt{3}-330 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+396\right) \left(\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}-\frac{1}{3}+\frac{17 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{12}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{11}\, \sqrt{3}}{4}\right)^{-n}}{264}\\-\frac{n^{2}}{2}-\frac{9 n}{2}-\frac{3}{2} & \mathit{\text{otherwise}} \end{array}\right.

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 50
a(6) = 112
a(7) = 234
a(n+3) = n^2+a(n)+a(n+1)+a(n+2)+9*n+1, n >= 8

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) = 19
a \! \left(5\right) = 50
a \! \left(6\right) = 112
a \! \left(7\right) = 234
a \! \left(n +3\right) = n^{2}+a \! \left(n \right)+a \! \left(n +1\right)+a \! \left(n +2\right)+9 n +1, \quad n \geq 8

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19483/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[21,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[11,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[19,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[16,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[18,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = F[15,x]+F[23,x]+F[53,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[39,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[15,x]+F[27,x]+F[32,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[17,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[11,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[20,x]+F[34,x]
F[34,x] = F[18,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[18,x]+F[38,x]
F[38,x] = F[36,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[2,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[17,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[2,x]+F[46,x]
F[56,x] = F[46,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[14,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[37,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{21}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)+F_{53}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{39}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)+F_{32}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{17}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{17}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right)+F_{46}\! \left(x \right)
F_{56}\! \left(x \right) = F_{46}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{37}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_21(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_11(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_19(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_16(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_18(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), F_15(x) + F_23(x) + F_53(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_39(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_15(x) + F_27(x) + F_32(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_17(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_11(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_20(x) + F_34(x))
Eq(F_34(x), F_18(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_18(x) + F_38(x))
Eq(F_38(x), F_36(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_2(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_17(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_2(x) + F_46(x))
Eq(F_56(x), F_46(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_14(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_37(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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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], "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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [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, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 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, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [[0, 1]]}], "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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [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, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [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], "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": [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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"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, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"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": [[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], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 2]], [[1, 0], [1, 1], [1, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, "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": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "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, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 2]]}], "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, 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], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], "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": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "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": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"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]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "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": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "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": [[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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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": [[0, 2]]}, {"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]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "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], [1, 2]]], "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": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "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": [[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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"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, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "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": [[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], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 2]], [[1, 0], [1, 1], [1, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, "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": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 2]]}], "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], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 2]], [[1, 0], [1, 1], [1, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 3]], [[1, 0], [1, 1], [1, 2], [1, 4]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 4], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[1, 4]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2], [1, 3], [1, 4]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "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": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "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], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"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]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1], [1, 2], [1, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "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": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[1, 4]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2], [1, 3], [1, 4]]], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": 2, "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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": 2, "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, 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": 2, "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"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": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 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": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 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": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}, {"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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "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], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "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": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"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, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "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, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [[0, 1]]}], "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": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 4], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 4]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}], "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, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 1]]}], "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": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 2]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 2]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 4], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[1, 4]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"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": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}], "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": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}], "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, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 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, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"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]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"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": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"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": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 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": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 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": [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, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "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, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"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]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"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": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[1, 4]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"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": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}], "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": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}], "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, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 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, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"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]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"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": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}], "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"}}]}