0132_1320

Counting sequence:
1, 1, 2, 6, 22, 88, 363, 1507, 6241, 25721, 105485, 430767, 1752945, 7113095, 28797292, 116368938, 469531170, 1892133076, 7617145998, 30638026074, 123145086046, 494663313342, 1985995240464, 7969941119476, 31971818819844, 128214549263032, 514024475597524, 2060262910065740, 8255954041620260, 33077227352665956, 132500624336147295, 530691534207329339, 2125245322390667449, 8509909701589556721, 34071816666157992953, 136403298374142890155, 546031746579866205541, 2185637046734801288491, 8747995978018019183423, 35011632752454866032521, 140117365693230924247015, 560724640185319574378833, 2243816916372725759627427, 8978568510065890839305145, 35926119250096585107217999, 143746900141999879472935677, 575139172906187070889598241, 2301096671849645376976260079, 9206303679409192796598104001, 36831991737178346894738618487, 147351804135473068794375976477, 589490545600063999869222046455, 2358251289878955336604995593409, 9433998852385357310763351595171, 37739370661232855559075747971625, 150968773429224963125239619314419, 603912103040723369250596828980117, 2415766350241535043968295021002559, 9663425980890572359138181145954681, 38654735411580227905314436314159979, 154621548680833691952066984162965661, 618491004807487443408986142121182111, 2473962472312615579761830328879122932, 9895766762704076284293475964318901690, 39582449698825051795294522916663427570, 158326274596082862831232622254973691364, 633287095041629801600559131516435473014, 2533061896896679933562870589291836664738, 10131848055095038280878824141575352762358, 40525595548838946562087172069095451102262, 162094460125865670505963547455609093729452, 648343428773036851599658324053457585650736, 2593225983980970630872862264956759492122296, 10372275682400789808468389892231525897241020, 41486451579572794713494884364921009336737960, 165934690760188644026796484887589188360903624, 663692411746046482225101075538622960461040424, 2654577261882743578623964610077582568302406848, 10617513734686967307202621647437203415240762298, 42466778601833113639092178733132085156023458402, 169853658568974915111450649501560682287183853462, 679359520341317150159864353752012704714246264726, 2717212879072390036269816040680191864186522135366, 10867933273553828787182044256648012087064991735890, 43467996189556257835333361086818051988512209493870, 173856803083021516541330232801123556292849083653074, 695365630451706107074433900278039725089334204390514, 2781213076669671152293473394787969343514244875219278, 11123843189578389295370982682912734284347918659390098, 44491295186907300187341216823635904913812557138041422, 177948721932696222173004778194809002458767304237172282, 711728517818976845520677341277093765714779337096931886, 2846646675708945855481358973473491704031038452441837666, 11385510290995159193205086503156810068927065468061754950, 45537711323133461955676517207130292566697886299922926600, 182133440863500826961375754142060168496702789391183368164, 728463849350886486501828350843270312142442689997594298484, 2913574719880750904712813658759241009741844724343749911528, 11653172701326989234969993638131790698958018955170602660028, 46608174530374002850131898489204275480010730612058133470612, 186414595433295742999132629089758075627931604308099219202492

Generating function in Maple syntax:
1/2*((-2*x^4+8*x^3-14*x^2+7*x-1)*(1-4*x)^(1/2)-2*x^4-16*x^3+24*x^2-9*x+1)/x^2/(4*x-1)/(x-1)^2

Generating function in latex syntax:
\frac{\left(-2 x^{4}+8 x^{3}-14 x^{2}+7 x -1\right) \sqrt{1-4 x}-2 x^{4}-16 x^{3}+24 x^{2}-9 x +1}{2 x^{2} \left(4 x -1\right) \left(x -1\right)^{2}}

Generating function in sympy syntax:
(-x**4 - 8*x**3 + 12*x**2 - 9*x/2 + sqrt(1 - 4*x)*(-2*x**4 + 8*x**3 - 14*x**2 + 7*x - 1)/2 + 1/2)/(x**2*(x - 1)**2*(4*x - 1))

Implicit equation for the generating function in Maple syntax:
x^2*(4*x-1)^2*(x-1)^4*F(x)^2+(4*x-1)*(2*x^4+16*x^3-24*x^2+9*x-1)*(x-1)^2*F(x)+4*x^7-32*x^6+144*x^5-242*x^4+192*x^3-75*x^2+14*x-1 = 0

Implicit equation for the generating function in latex syntax:
x^{2} \left(4 x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)^{2}+\left(4 x -1\right) \left(2 x^{4}+16 x^{3}-24 x^{2}+9 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+4 x^{7}-32 x^{6}+144 x^{5}-242 x^{4}+192 x^{3}-75 x^{2}+14 x -1 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 88
a(6) = 363
a(7) = 1507
a(n+7) = 16*(2*n+1)/(9+n)*a(n)+2*(217*n+708)/(9+n)*a(2+n)-4*(44*n+81)/(9+n)*a(n+1)-2*(261*n+1139)/(9+n)*a(n+3)+2*(159*n+871)/(9+n)*a(n+4)-(670+101*n)/(9+n)*a(n+5)+(16*n+125)/(9+n)*a(n+6)-32/(9+n), 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) = 22
a \! \left(5\right) = 88
a \! \left(6\right) = 363
a \! \left(7\right) = 1507
a \! \left(n +7\right) = \frac{16 \left(2 n +1\right) a \! \left(n \right)}{9+n}+\frac{2 \left(217 n +708\right) a \! \left(2+n \right)}{9+n}-\frac{4 \left(44 n +81\right) a \! \left(n +1\right)}{9+n}-\frac{2 \left(261 n +1139\right) a \! \left(n +3\right)}{9+n}+\frac{2 \left(159 n +871\right) a \! \left(n +4\right)}{9+n}-\frac{\left(670+101 n \right) a \! \left(n +5\right)}{9+n}+\frac{\left(16 n +125\right) a \! \left(n +6\right)}{9+n}-\frac{32}{9+n}, \quad n \geq 8

Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://permpal.com/tree/82/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[6,x]
F[1,x] = F[2,x]+F[3,x]
F[2,x] = 1
F[3,x] = F[4,x]
F[4,x] = F[1,x]*F[5,x]
F[5,x] = x
F[6,x] = F[7,x]
F[7,x] = F[1,x]*F[5,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[5,x]
F[10,x] = F[11,x]+F[38,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]+F[22,x]
F[13,x] = F[14,x]+F[20,x]
F[14,x] = F[0,x]*F[15,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x]*F[5,x]
F[17,x] = F[15,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[15,x]*F[17,x]*F[5,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[15,x]*F[5,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[5,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[1,x]*F[12,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[31,x]*F[36,x]
F[28,x] = F[29,x]+F[34,x]
F[29,x] = F[30,x]
F[30,x] = F[17,x]*F[31,x]
F[31,x] = F[2,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]*F[5,x]
F[34,x] = F[35,x]
F[35,x] = F[17,x]*F[28,x]*F[32,x]*F[5,x]
F[36,x] = F[37,x]
F[37,x] = F[15,x]*F[17,x]*F[3,x]*F[5,x]
F[38,x] = F[39,x]
F[39,x] = F[15,x]*F[40,x]*F[5,x]
F[40,x] = F[41,x]
F[41,x] = F[17,x]^2*F[42,x]*F[5,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[28,x]*F[31,x]
F[44,x] = F[45,x]
F[45,x] = F[40,x]*F[5,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{1}\! \left(x \right) = F_{2}\! \left(x \right)+F_{3}\! \left(x \right)
F_{2}\! \left(x \right) = 1
F_{3}\! \left(x \right) = F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{22}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{20}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{5}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right) F_{12}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{36}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{34}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31}\! \left(x \right) F_{5}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right) F_{28}\! \left(x \right) F_{32}\! \left(x \right) F_{5}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right) F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{40}\! \left(x \right) F_{5}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{42}\! \left(x \right) F_{5}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{40}\! \left(x \right) F_{5}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_6(x))
Eq(F_1(x), F_2(x) + F_3(x))
Eq(F_2(x), 1)
Eq(F_3(x), F_4(x))
Eq(F_4(x), F_1(x)*F_5(x))
Eq(F_5(x), x)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_1(x)*F_5(x)*F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_5(x))
Eq(F_10(x), F_11(x) + F_38(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x) + F_22(x))
Eq(F_13(x), F_14(x) + F_20(x))
Eq(F_14(x), F_0(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x)*F_5(x))
Eq(F_17(x), F_15(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_15(x)*F_17(x)*F_5(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_15(x)*F_5(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_5(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_1(x)*F_12(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_31(x)*F_36(x))
Eq(F_28(x), F_29(x) + F_34(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_17(x)*F_31(x))
Eq(F_31(x), F_2(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)*F_5(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_17(x)*F_28(x)*F_32(x)*F_5(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_15(x)*F_17(x)*F_3(x)*F_5(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_15(x)*F_40(x)*F_5(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_17(x)**2*F_42(x)*F_5(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_28(x)*F_31(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_40(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 2, "strategy_class": "RequirementInsertionFactory"}, {"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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "requirement_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 0], [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": [1, 3, 2, 0], "pos": [[0, 0], 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[0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[4, 3], [4, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [4, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 2]]}], [{"patt": [0], "pos": [[3, 0]]}]]}], "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], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [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": [1, 3, 2, 0], "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": [[1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}]}

Specification 2
Strategy pack name: insertion_col_placements_tracked_fusion
Tree: http://permpal.com/tree/83/
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[6,x]+F[9,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[6,x]^2*F[4,x]
F[9,x] = F[10,x]+F[2,x]
F[10,x] = F[11,x]+F[12,x]+F[239,x]
F[11,x] = 0
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x,k[0]]*F[4,x]
F[14,x,k[0]] = F[15,x,k[0]]+F[29,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[19,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[20,x,k[0]] = F[11,x]+F[21,x,k[0]]+F[27,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[4,x]
F[22,x,k[0]] = F[23,x,k[0]]+F[26,x,k[0]]
F[23,x,k[0]] = F[16,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[26,x,k[0]] = -k[0]*(F[20,x,1]-F[20,x,k[0]])/(-1+k[0])
F[27,x,k[0]] = F[18,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[20,x,k[0]]+F[7,x]
F[29,x,k[0]] = F[30,x,k[0]]+F[67,x,k[0]]
F[30,x,k[0]] = F[11,x]+F[31,x,k[0]]+F[65,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[4,x]
F[32,x,k[0]] = F[33,x,k[0]]+F[35,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0]]*F[6,x]
F[35,x,k[0]] = F[30,x,k[0]]+F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[4,x]
F[38,x,k[0]] = F[39,x,k[0]]+F[56,x,k[0]]
F[39,x,k[0]] = F[30,x,k[0]]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = 2*F[11,x]+F[42,x,k[0]]+F[46,x,k[0]]
F[42,x,k[0]] = F[4,x]*F[43,x,k[0]]
F[43,x,k[0]] = F[41,x,k[0]]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[16,x,k[0]]*F[7,x]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[18,x,k[0]]*F[48,x,k[0]]*F[7,x]
F[48,x,k[0]] = F[49,x]+F[52,x,k[0]]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[1,x]+F[49,x]
F[52,x,k[0]] = F[11,x]+F[53,x,k[0]]+F[55,x,k[0]]
F[53,x,k[0]] = F[4,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[16,x,k[0]]+F[52,x,k[0]]
F[55,x,k[0]] = F[18,x,k[0]]*F[48,x,k[0]]
F[56,x,k[0]] = F[36,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = 3*F[11,x]+F[58,x,k[0]]+F[63,x,k[0]]
F[58,x,k[0]] = F[4,x]*F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[62,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[7,x]^2*F[16,x,k[0]]
F[62,x,k[0]] = F[57,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[7,x]^2*F[18,x,k[0]]*F[48,x,k[0]]
F[65,x,k[0]] = F[18,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[2,x]+F[30,x,k[0]]
F[67,x,k[0]] = F[11,x]+F[236,x,k[0]]+F[238,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[72,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[20,x,k[0]]*F[6,x]
F[72,x,k[0]] = F[220,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[11,x]+F[195,x,k[0]]+F[205,x,k[0]]+F[74,x,k[0]]
F[74,x,k[0]] = F[4,x]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[90,x,k[0]]
F[76,x,k[0]] = (-F[77,x,1]*k[0]+F[77,x,k[0]])/(-1+k[0])
F[77,x,k[0]] = F[78,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[16,x,k[0]]*F[18,x,k[0]]
F[80,x,k[0]] = F[11,x]+F[81,x,k[0]]+F[83,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[4,x]*F[77,x,k[0]]
F[83,x,k[0]] = F[18,x,k[0]]*F[84,x,k[0]]
F[84,x,k[0]] = F[11,x]+F[85,x,k[0]]+F[88,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[4,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[16,x,k[0]]+F[84,x,k[0]]
F[88,x,k[0]] = F[18,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = F[7,x]+F[84,x,k[0]]
F[90,x,k[0]] = (-F[91,x,1]*k[0]+F[91,x,k[0]])/(-1+k[0])
F[91,x,k[0]] = F[92,x,k[0]]+F[96,x,k[0]]
F[92,x,k[0]] = F[11,x]+F[93,x,k[0]]+F[95,x,k[0]]
F[93,x,k[0]] = F[4,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[77,x,k[0]]+F[91,x,k[0]]
F[95,x,k[0]] = F[18,x,k[0]]*F[52,x,k[0]]
F[96,x,k[0]] = F[11,x]+F[118,x,k[0]]+F[120,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[4,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[101,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]
F[100,x,k[0]] = F[6,x]*F[7,x]*F[78,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[110,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = 2*F[11,x]+F[104,x,k[0]]+F[108,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[4,x]
F[105,x,k[0]] = F[103,x,k[0]]+F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[7,x]*F[78,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[18,x,k[0]]*F[52,x,k[0]]*F[7,x]
F[110,x,k[0]] = 3*F[11,x]+F[111,x,k[0]]+F[116,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[4,x]
F[112,x,k[0]] = F[113,x,k[0]]+F[115,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[7,x]^2*F[78,x,k[0]]
F[115,x,k[0]] = F[110,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[7,x]^2*F[18,x,k[0]]*F[52,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[4,x]*F[91,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[18,x,k[0]]
F[121,x,k[0]] = F[11,x]+F[122,x,k[0]]+F[127,x,k[0]]+F[130,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]*F[4,x]
F[123,x,k[0]] = F[124,x,k[0]]+F[126,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[16,x,k[0]]*F[6,x]*F[7,x]
F[126,x,k[0]] = F[40,x,k[0]]+F[57,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[4,x]
F[129,x,k[0]] = F[121,x,k[0]]+F[30,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[18,x,k[0]]
F[131,x,k[0]] = F[121,x,k[0]]+F[132,x]
F[132,x] = F[11,x]+F[133,x]+F[188,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[135,x]+F[137,x]
F[135,x] = F[136,x]
F[136,x] = F[6,x]*F[7,x]
F[137,x] = F[138,x]+F[175,x]
F[138,x] = F[11,x]+F[139,x]+F[142,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[141,x,1]
F[141,x,k[0]] = F[129,x,k[0]]+F[87,x,k[0]]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[155,x]
F[144,x] = F[145,x]+F[49,x]
F[145,x] = F[11,x]+F[142,x]+F[146,x]
F[146,x] = F[147,x]*F[4,x]
F[147,x] = F[148,x]+F[151,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[1,x]+F[148,x]
F[151,x] = F[11,x]+F[152,x]+F[153,x]
F[152,x] = F[147,x]*F[4,x]
F[153,x] = F[154,x]*F[4,x]
F[154,x] = F[151,x]+F[49,x]
F[155,x] = F[145,x]+F[156,x]
F[156,x] = F[157,x]
F[157,x] = 2*F[11,x]+F[158,x]+F[163,x]
F[158,x] = F[159,x]*F[4,x]
F[159,x] = F[160,x]+F[162,x]
F[160,x] = F[161,x]
F[161,x] = F[7,x]^2
F[162,x] = F[157,x]
F[163,x] = F[164,x]
F[164,x] = F[165,x]*F[4,x]*F[7,x]
F[165,x] = F[154,x]+F[166,x]
F[166,x] = F[167,x,1]
F[167,x,k[0]] = F[168,x]+F[170,x,k[0]]
F[168,x] = F[169,x]
F[169,x] = F[49,x]*F[7,x]
F[170,x,k[0]] = 2*F[11,x]+F[171,x,k[0]]+F[174,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]*F[4,x]*F[6,x]
F[173,x,k[0]] = F[170,x,k[0]]+F[52,x,k[0]]
F[174,x,k[0]] = F[167,x,k[0]]*F[18,x,k[0]]
F[175,x] = F[176,x]
F[176,x] = F[177,x]*F[4,x]
F[177,x] = F[178,x]+F[179,x]
F[178,x] = F[138,x]+F[157,x]
F[179,x] = F[175,x]+F[180,x]
F[180,x] = 3*F[11,x]+F[181,x]+F[186,x]
F[181,x] = F[182,x]*F[4,x]
F[182,x] = F[183,x]+F[185,x]
F[183,x] = F[184,x]
F[184,x] = F[7,x]^3
F[185,x] = F[180,x]
F[186,x] = F[187,x]
F[187,x] = F[7,x]^2*F[165,x]*F[4,x]
F[188,x] = F[189,x]*F[4,x]
F[189,x] = F[190,x]+F[193,x]
F[190,x] = F[191,x]+F[2,x]
F[191,x] = F[11,x]+F[139,x]+F[192,x]
F[192,x] = F[154,x]*F[4,x]
F[193,x] = F[194,x,1]
F[194,x,k[0]] = F[132,x]+F[67,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[4,x]
F[196,x,k[0]] = F[197,x,k[0]]+F[207,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[52,x,k[0]]
F[198,x,k[0]] = F[11,x]+F[195,x,k[0]]+F[199,x,k[0]]+F[205,x,k[0]]
F[199,x,k[0]] = (-F[200,x,1]*k[0]+F[200,x,k[0]])/(-1+k[0])
F[200,x,k[0]] = F[201,x,k[0]]*F[4,x]
F[201,x,k[0]] = F[202,x,k[0]]+F[78,x,k[0]]
F[202,x,k[0]] = F[11,x]+F[203,x,k[0]]+F[204,x,k[0]]
F[203,x,k[0]] = F[201,x,k[0]]*F[4,x]
F[204,x,k[0]] = F[18,x,k[0]]*F[52,x,k[0]]
F[205,x,k[0]] = F[18,x,k[0]]*F[206,x,k[0]]
F[206,x,k[0]] = F[145,x]+F[198,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[41,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]
F[209,x,k[0]] = 2*F[11,x]+F[210,x,k[0]]+F[215,x,k[0]]+F[218,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]*F[4,x]
F[211,x,k[0]] = F[212,x,k[0]]+F[214,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[20,x,k[0]]*F[7,x]
F[214,x,k[0]] = F[209,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]
F[216,x,k[0]] = -k[0]*(F[217,x,1]-F[217,x,k[0]])/(-1+k[0])
F[217,x,k[0]] = F[173,x,k[0]]*F[4,x]*F[7,x]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = F[167,x,k[0]]*F[18,x,k[0]]*F[7,x]
F[220,x,k[0]] = F[221,x,k[0]]
F[221,x,k[0]] = F[222,x,k[0]]*F[4,x]
F[222,x,k[0]] = F[223,x,k[0]]+F[224,x,k[0]]
F[223,x,k[0]] = F[209,x,k[0]]+F[73,x,k[0]]
F[224,x,k[0]] = F[220,x,k[0]]+F[225,x,k[0]]
F[225,x,k[0]] = 3*F[11,x]+F[226,x,k[0]]+F[231,x,k[0]]+F[234,x,k[0]]
F[226,x,k[0]] = F[227,x,k[0]]*F[4,x]
F[227,x,k[0]] = F[228,x,k[0]]+F[230,x,k[0]]
F[228,x,k[0]] = F[229,x,k[0]]
F[229,x,k[0]] = F[7,x]^2*F[20,x,k[0]]
F[230,x,k[0]] = F[225,x,k[0]]
F[231,x,k[0]] = F[232,x,k[0]]
F[232,x,k[0]] = -k[0]*(F[233,x,1]-F[233,x,k[0]])/(-1+k[0])
F[233,x,k[0]] = F[7,x]^2*F[173,x,k[0]]*F[4,x]
F[234,x,k[0]] = F[235,x,k[0]]
F[235,x,k[0]] = F[7,x]^2*F[167,x,k[0]]*F[18,x,k[0]]
F[236,x,k[0]] = -k[0]*(F[237,x,1]-F[237,x,k[0]])/(-1+k[0])
F[237,x,k[0]] = F[29,x,k[0]]*F[4,x]
F[238,x,k[0]] = F[18,x,k[0]]*F[194,x,k[0]]
F[239,x] = F[240,x]*F[4,x]
F[240,x] = F[241,x]+F[242,x]
F[241,x] = F[138,x]+F[2,x]
F[242,x] = F[10,x]+F[175,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_{6}\! \left(x \right)+F_{9}\! \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_{6} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)+F_{239}\! \left(x \right)
F_{11}\! \left(x \right) = 0
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = -\frac{y \left(F_{20}\! \left(x , 1\right)-F_{20}\! \left(x , y\right)\right)}{-1+y}
F_{27}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = 2 F_{11}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{48}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{53}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = 3 F_{11}\! \left(x \right)+F_{58}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{7} \left(x \right)^{2} F_{16}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{7} \left(x \right)^{2} F_{18}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{236}\! \left(x , y\right)+F_{238}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{220}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{195}\! \left(x , y\right)+F_{205}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = -\frac{F_{77}\! \left(x , 1\right) y -F_{77}\! \left(x , y\right)}{-1+y}
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{81}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{85}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{7}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = -\frac{F_{91}\! \left(x , 1\right) y -F_{91}\! \left(x , y\right)}{-1+y}
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{118}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{7}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = 2 F_{11}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{52}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{110}\! \left(x , y\right) = 3 F_{11}\! \left(x \right)+F_{111}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{7} \left(x \right)^{2} F_{78}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{7} \left(x \right)^{2} F_{18}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{122}\! \left(x , y\right)+F_{127}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{6}\! \left(x \right) F_{7}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{11}\! \left(x \right)+F_{133}\! \left(x \right)+F_{188}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{137}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{6}\! \left(x \right) F_{7}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{175}\! \left(x \right)
F_{138}\! \left(x \right) = F_{11}\! \left(x \right)+F_{139}\! \left(x \right)+F_{142}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x , 1\right)
F_{141}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{155}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{49}\! \left(x \right)
F_{145}\! \left(x \right) = F_{11}\! \left(x \right)+F_{142}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{151}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{1}\! \left(x \right)+F_{148}\! \left(x \right)
F_{151}\! \left(x \right) = F_{11}\! \left(x \right)+F_{152}\! \left(x \right)+F_{153}\! \left(x \right)
F_{152}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{4}\! \left(x \right)
F_{154}\! \left(x \right) = F_{151}\! \left(x \right)+F_{49}\! \left(x \right)
F_{155}\! \left(x \right) = F_{145}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = 2 F_{11}\! \left(x \right)+F_{158}\! \left(x \right)+F_{163}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{4}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{162}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{7} \left(x \right)^{2}
F_{162}\! \left(x \right) = F_{157}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{165}\! \left(x \right) = F_{154}\! \left(x \right)+F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x , 1\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x \right)+F_{170}\! \left(x , y\right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{49}\! \left(x \right) F_{7}\! \left(x \right)
F_{170}\! \left(x , y\right) = 2 F_{11}\! \left(x \right)+F_{171}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right) F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{4}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{179}\! \left(x \right)
F_{178}\! \left(x \right) = F_{138}\! \left(x \right)+F_{157}\! \left(x \right)
F_{179}\! \left(x \right) = F_{175}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = 3 F_{11}\! \left(x \right)+F_{181}\! \left(x \right)+F_{186}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right) F_{4}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{185}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{7} \left(x \right)^{3}
F_{185}\! \left(x \right) = F_{180}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{7} \left(x \right)^{2} F_{165}\! \left(x \right) F_{4}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right) F_{4}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{193}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{2}\! \left(x \right)
F_{191}\! \left(x \right) = F_{11}\! \left(x \right)+F_{139}\! \left(x \right)+F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{154}\! \left(x \right) F_{4}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x , 1\right)
F_{194}\! \left(x , y\right) = F_{132}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{195}\! \left(x , y\right)+F_{199}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = -\frac{F_{200}\! \left(x , 1\right) y -F_{200}\! \left(x , y\right)}{-1+y}
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{203}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{204}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{145}\! \left(x \right)+F_{198}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = 2 F_{11}\! \left(x \right)+F_{210}\! \left(x , y\right)+F_{215}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{214}\! \left(x , y\right) = F_{209}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = -\frac{y \left(F_{217}\! \left(x , 1\right)-F_{217}\! \left(x , y\right)\right)}{-1+y}
F_{217}\! \left(x , y\right) = F_{173}\! \left(x , y\right) F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{224}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{220}\! \left(x , y\right)+F_{225}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = 3 F_{11}\! \left(x \right)+F_{226}\! \left(x , y\right)+F_{231}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{227}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{227}\! \left(x , y\right) = F_{228}\! \left(x , y\right)+F_{230}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{229}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{7} \left(x \right)^{2} F_{20}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{225}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = -\frac{y \left(F_{233}\! \left(x , 1\right)-F_{233}\! \left(x , y\right)\right)}{-1+y}
F_{233}\! \left(x , y\right) = F_{7} \left(x \right)^{2} F_{173}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{234}\! \left(x , y\right) = F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{7} \left(x \right)^{2} F_{167}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = -\frac{y \left(F_{237}\! \left(x , 1\right)-F_{237}\! \left(x , y\right)\right)}{-1+y}
F_{237}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{238}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{194}\! \left(x , y\right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right) F_{4}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)+F_{242}\! \left(x \right)
F_{241}\! \left(x \right) = F_{138}\! \left(x \right)+F_{2}\! \left(x \right)
F_{242}\! \left(x \right) = F_{10}\! \left(x \right)+F_{175}\! \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_6(x) + F_9(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_6(x)**2)
Eq(F_9(x), F_10(x) + F_2(x))
Eq(F_10(x), F_11(x) + F_12(x) + F_239(x))
Eq(F_11(x), 0)
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x, k_0)*F_4(x))
Eq(F_14(x, k_0), F_15(x, k_0) + F_29(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_19(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_20(x, k_0), F_11(x) + F_21(x, k_0) + F_27(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_4(x))
Eq(F_22(x, k_0), F_23(x, k_0) + F_26(x, k_0))
Eq(F_23(x, k_0), F_16(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_26(x, k_0), -F_20(x, 1) + (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_27(x, k_0), F_18(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_20(x, k_0) + F_7(x))
Eq(F_29(x, k_0), F_30(x, k_0) + F_67(x, k_0))
Eq(F_30(x, k_0), F_11(x) + F_31(x, k_0) + F_65(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_4(x))
Eq(F_32(x, k_0), F_33(x, k_0) + F_35(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0)*F_6(x))
Eq(F_35(x, k_0), F_30(x, k_0) + F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_4(x))
Eq(F_38(x, k_0), F_39(x, k_0) + F_56(x, k_0))
Eq(F_39(x, k_0), F_30(x, k_0) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), 2*F_11(x) + F_42(x, k_0) + F_46(x, k_0))
Eq(F_42(x, k_0), F_4(x)*F_43(x, k_0))
Eq(F_43(x, k_0), F_41(x, k_0) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_16(x, k_0)*F_7(x))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_18(x, k_0)*F_48(x, k_0)*F_7(x))
Eq(F_48(x, k_0), F_49(x) + F_52(x, k_0))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_1(x) + F_49(x))
Eq(F_52(x, k_0), F_11(x) + F_53(x, k_0) + F_55(x, k_0))
Eq(F_53(x, k_0), F_4(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_16(x, k_0) + F_52(x, k_0))
Eq(F_55(x, k_0), F_18(x, k_0)*F_48(x, k_0))
Eq(F_56(x, k_0), F_36(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), 3*F_11(x) + F_58(x, k_0) + F_63(x, k_0))
Eq(F_58(x, k_0), F_4(x)*F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_62(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_16(x, k_0)*F_7(x)**2)
Eq(F_62(x, k_0), F_57(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_18(x, k_0)*F_48(x, k_0)*F_7(x)**2)
Eq(F_65(x, k_0), F_18(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_2(x) + F_30(x, k_0))
Eq(F_67(x, k_0), F_11(x) + F_236(x, k_0) + F_238(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_72(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_20(x, k_0)*F_6(x))
Eq(F_72(x, k_0), F_220(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_11(x) + F_195(x, k_0) + F_205(x, k_0) + F_74(x, k_0))
Eq(F_74(x, k_0), F_4(x)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_90(x, k_0))
Eq(F_76(x, k_0), -F_77(x, 1) - F_77(x, k_0) + (k_0*F_77(x, k_0) - F_77(x, 1))/(k_0 - 1))
Eq(F_77(x, k_0), F_78(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_16(x, k_0)*F_18(x, k_0))
Eq(F_80(x, k_0), F_11(x) + F_81(x, k_0) + F_83(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_4(x)*F_77(x, k_0))
Eq(F_83(x, k_0), F_18(x, k_0)*F_84(x, k_0))
Eq(F_84(x, k_0), F_11(x) + F_85(x, k_0) + F_88(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_4(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_16(x, k_0) + F_84(x, k_0))
Eq(F_88(x, k_0), F_18(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), F_7(x) + F_84(x, k_0))
Eq(F_90(x, k_0), -F_91(x, 1) - F_91(x, k_0) + (k_0*F_91(x, k_0) - F_91(x, 1))/(k_0 - 1))
Eq(F_91(x, k_0), F_92(x, k_0) + F_96(x, k_0))
Eq(F_92(x, k_0), F_11(x) + F_93(x, k_0) + F_95(x, k_0))
Eq(F_93(x, k_0), F_4(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_77(x, k_0) + F_91(x, k_0))
Eq(F_95(x, k_0), F_18(x, k_0)*F_52(x, k_0))
Eq(F_96(x, k_0), F_11(x) + F_118(x, k_0) + F_120(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_4(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_101(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0))
Eq(F_100(x, k_0), F_6(x)*F_7(x)*F_78(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_110(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_108(x, k_0) + 2*F_11(x))
Eq(F_104(x, k_0), F_105(x, k_0)*F_4(x))
Eq(F_105(x, k_0), F_103(x, k_0) + F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_7(x)*F_78(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_18(x, k_0)*F_52(x, k_0)*F_7(x))
Eq(F_110(x, k_0), 3*F_11(x) + F_111(x, k_0) + F_116(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_4(x))
Eq(F_112(x, k_0), F_113(x, k_0) + F_115(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_7(x)**2*F_78(x, k_0))
Eq(F_115(x, k_0), F_110(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_18(x, k_0)*F_52(x, k_0)*F_7(x)**2)
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_4(x)*F_91(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_18(x, k_0))
Eq(F_121(x, k_0), F_11(x) + F_122(x, k_0) + F_127(x, k_0) + F_130(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0)*F_4(x))
Eq(F_123(x, k_0), F_124(x, k_0) + F_126(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_16(x, k_0)*F_6(x)*F_7(x))
Eq(F_126(x, k_0), F_40(x, k_0) + F_57(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_4(x))
Eq(F_129(x, k_0), F_121(x, k_0) + F_30(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_18(x, k_0))
Eq(F_131(x, k_0), F_121(x, k_0) + F_132(x))
Eq(F_132(x), F_11(x) + F_133(x) + F_188(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_135(x) + F_137(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_6(x)*F_7(x))
Eq(F_137(x), F_138(x) + F_175(x))
Eq(F_138(x), F_11(x) + F_139(x) + F_142(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_141(x, 1))
Eq(F_141(x, k_0), F_129(x, k_0) + F_87(x, k_0))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_155(x))
Eq(F_144(x), F_145(x) + F_49(x))
Eq(F_145(x), F_11(x) + F_142(x) + F_146(x))
Eq(F_146(x), F_147(x)*F_4(x))
Eq(F_147(x), F_148(x) + F_151(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_1(x) + F_148(x))
Eq(F_151(x), F_11(x) + F_152(x) + F_153(x))
Eq(F_152(x), F_147(x)*F_4(x))
Eq(F_153(x), F_154(x)*F_4(x))
Eq(F_154(x), F_151(x) + F_49(x))
Eq(F_155(x), F_145(x) + F_156(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), 2*F_11(x) + F_158(x) + F_163(x))
Eq(F_158(x), F_159(x)*F_4(x))
Eq(F_159(x), F_160(x) + F_162(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_7(x)**2)
Eq(F_162(x), F_157(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_165(x)*F_4(x)*F_7(x))
Eq(F_165(x), F_154(x) + F_166(x))
Eq(F_166(x), F_167(x, 1))
Eq(F_167(x, k_0), F_168(x) + F_170(x, k_0))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_49(x)*F_7(x))
Eq(F_170(x, k_0), 2*F_11(x) + F_171(x, k_0) + F_174(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0)*F_4(x)*F_6(x))
Eq(F_173(x, k_0), F_170(x, k_0) + F_52(x, k_0))
Eq(F_174(x, k_0), F_167(x, k_0)*F_18(x, k_0))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_177(x)*F_4(x))
Eq(F_177(x), F_178(x) + F_179(x))
Eq(F_178(x), F_138(x) + F_157(x))
Eq(F_179(x), F_175(x) + F_180(x))
Eq(F_180(x), 3*F_11(x) + F_181(x) + F_186(x))
Eq(F_181(x), F_182(x)*F_4(x))
Eq(F_182(x), F_183(x) + F_185(x))
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_7(x)**3)
Eq(F_185(x), F_180(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_165(x)*F_4(x)*F_7(x)**2)
Eq(F_188(x), F_189(x)*F_4(x))
Eq(F_189(x), F_190(x) + F_193(x))
Eq(F_190(x), F_191(x) + F_2(x))
Eq(F_191(x), F_11(x) + F_139(x) + F_192(x))
Eq(F_192(x), F_154(x)*F_4(x))
Eq(F_193(x), F_194(x, 1))
Eq(F_194(x, k_0), F_132(x) + F_67(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_4(x))
Eq(F_196(x, k_0), F_197(x, k_0) + F_207(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_52(x, k_0))
Eq(F_198(x, k_0), F_11(x) + F_195(x, k_0) + F_199(x, k_0) + F_205(x, k_0))
Eq(F_199(x, k_0), -F_200(x, 1) - F_200(x, k_0) + (k_0*F_200(x, k_0) - F_200(x, 1))/(k_0 - 1))
Eq(F_200(x, k_0), F_201(x, k_0)*F_4(x))
Eq(F_201(x, k_0), F_202(x, k_0) + F_78(x, k_0))
Eq(F_202(x, k_0), F_11(x) + F_203(x, k_0) + F_204(x, k_0))
Eq(F_203(x, k_0), F_201(x, k_0)*F_4(x))
Eq(F_204(x, k_0), F_18(x, k_0)*F_52(x, k_0))
Eq(F_205(x, k_0), F_18(x, k_0)*F_206(x, k_0))
Eq(F_206(x, k_0), F_145(x) + F_198(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_41(x, k_0))
Eq(F_208(x, k_0), F_209(x, k_0))
Eq(F_209(x, k_0), 2*F_11(x) + F_210(x, k_0) + F_215(x, k_0) + F_218(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0)*F_4(x))
Eq(F_211(x, k_0), F_212(x, k_0) + F_214(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_20(x, k_0)*F_7(x))
Eq(F_214(x, k_0), F_209(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0))
Eq(F_216(x, k_0), -F_217(x, 1) + (k_0*F_217(x, k_0) - F_217(x, 1))/(k_0 - 1))
Eq(F_217(x, k_0), F_173(x, k_0)*F_4(x)*F_7(x))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), F_167(x, k_0)*F_18(x, k_0)*F_7(x))
Eq(F_220(x, k_0), F_221(x, k_0))
Eq(F_221(x, k_0), F_222(x, k_0)*F_4(x))
Eq(F_222(x, k_0), F_223(x, k_0) + F_224(x, k_0))
Eq(F_223(x, k_0), F_209(x, k_0) + F_73(x, k_0))
Eq(F_224(x, k_0), F_220(x, k_0) + F_225(x, k_0))
Eq(F_225(x, k_0), 3*F_11(x) + F_226(x, k_0) + F_231(x, k_0) + F_234(x, k_0))
Eq(F_226(x, k_0), F_227(x, k_0)*F_4(x))
Eq(F_227(x, k_0), F_228(x, k_0) + F_230(x, k_0))
Eq(F_228(x, k_0), F_229(x, k_0))
Eq(F_229(x, k_0), F_20(x, k_0)*F_7(x)**2)
Eq(F_230(x, k_0), F_225(x, k_0))
Eq(F_231(x, k_0), F_232(x, k_0))
Eq(F_232(x, k_0), -F_233(x, 1) + (k_0*F_233(x, k_0) - F_233(x, 1))/(k_0 - 1))
Eq(F_233(x, k_0), F_173(x, k_0)*F_4(x)*F_7(x)**2)
Eq(F_234(x, k_0), F_235(x, k_0))
Eq(F_235(x, k_0), F_167(x, k_0)*F_18(x, k_0)*F_7(x)**2)
Eq(F_236(x, k_0), -F_237(x, 1) + (k_0*F_237(x, k_0) - F_237(x, 1))/(k_0 - 1))
Eq(F_237(x, k_0), F_29(x, k_0)*F_4(x))
Eq(F_238(x, k_0), F_18(x, k_0)*F_194(x, k_0))
Eq(F_239(x), F_240(x)*F_4(x))
Eq(F_240(x), F_241(x) + F_242(x))
Eq(F_241(x), F_138(x) + F_2(x))
Eq(F_242(x), F_10(x) + F_175(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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": [1, 3, 2, 0], "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": [1, 3, 2, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 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"}}, {"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"}}, {"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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [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]]}], "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": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"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": [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]]}], "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]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [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]]}], "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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [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]]}], "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": [1, 3, 2, 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, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [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]]}], "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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [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]]}], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 3], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 0]]}, {"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": [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": [1, 3, 2, 0], "pos": [[0, 0], [0, 3], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}], "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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, 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