0231_3102

Counting sequence:
1, 1, 2, 6, 22, 86, 338, 1318, 5106, 19718, 76066, 293398, 1131794, 4366374, 16846018, 64995254, 250765298, 967503814, 3732821922, 14401956182, 55565542354, 214382633062, 827129764994, 3191227078902, 12312373271986, 47503525349126, 183277819294562, 707121393512086, 2728211558369682, 10525969619710886, 40611233423076418, 156686019406027318, 604525068754863986, 2332375027077989958, 8998755466272237346, 34718944853111536598, 133952426669653342034, 516814456389832646374, 1993970463799070688258, 7693124991658179801974, 29681569116380836575538, 114517253543360779623814, 441829786952766666236642, 1704665057871054855676182, 6576928594081366457625874, 25375066809703511053853222, 97901931940748525080830914, 377724651903801142603474102, 1457335006853562307962172146, 5622681261327280231157501126, 21693395422331788872040015522, 83697329277127830762740948566, 322920538336408427853217721042, 1245890101632813203796679114086, 4806885784791875717640965376898, 18545898163692142285340411555318, 71553674061954362064461429798066, 276067959964745016552852153275398, 1065123762241852096533464919536226, 4109454168593545634778641214894998, 15855071647473288715502838524899474, 61171943190826944330385640335454374, 236013227624745312634978465709964098, 910584832005184516067609866141290294, 3513212986503704564737772502897278578, 13554657462675596920920762552037913414, 52296498856253876417182821813329724962, 201770041047006119157081472442492756182, 778467973085775543900426268905191194194, 3003480506697690535780922422061578206182, 11588010638838507448904208923774553535234, 44708793769890887795613198126149711530102, 172495202382640041783718097780019610669106, 665519964554851444795559167533888433941126, 2567705171524619619963618942580202437222882, 9906704830837391340373422689494917042087446, 38221989694814888412790130034603316799427602, 147467853456480465583791813621452230182395686, 568959595685624827448020902058110405410435778, 2195156530289374992038625686259210555577211318, 8469339877580055600791553868689529818194127346, 32676356775574464709756033279123297403960900038, 126071725489627863918453298426745532004213900706, 486409181938327001717586915675241600434920096598, 1876661014633114402280785951889977330167616156114, 7240522372150316752340339654137411026666170358374, 27935340379977107401697379805819123382923199953538, 107779964211811206204058451742073958134745852052214, 415836017298917335429573375960050399922438026218418, 1604376050294474500159875122123725799321239068516614, 6189994141147715003904097548155181033113905893142882, 23882198603257845566827621091499165008877541167020182, 92142156699957401566167495320150669721770366870247314, 355502321304761823955756590059056041242889447435627942, 1371596943021549011685241752562347489161485297225189954, 5291887173060940941295956267747949819756981626862158902, 20417127637158161979135261292902382892714256323921130866, 78773240494257815684352370447110818794500295203513901126, 303922448262162977138296745717055412437539730082752996642, 1172591783429302616919419648481061113355173561998338016726, 4524086649170003087256286489876704763626726950624856065362

Generating function in Maple syntax:
-(8*x^3-11*x^2+6*x-1)/(4*x^4-16*x^3+16*x^2-7*x+1)

Generating function in latex syntax:
-\frac{8 x^{3}-11 x^{2}+6 x -1}{4 x^{4}-16 x^{3}+16 x^{2}-7 x +1}

Generating function in sympy syntax:
(-8*x**3 + 11*x**2 - 6*x + 1)/(4*x**4 - 16*x**3 + 16*x**2 - 7*x + 1)

Implicit equation for the generating function in Maple syntax:
(4*x^4-16*x^3+16*x^2-7*x+1)*F(x)+8*x^3-11*x^2+6*x-1 = 0

Implicit equation for the generating function in latex syntax:
\left(4 x^{4}-16 x^{3}+16 x^{2}-7 x +1\right) F \! \left(x \right)+8 x^{3}-11 x^{2}+6 x -1 = 0

Explicit closed form in Maple syntax:
40/571*Sum(_alpha^(-n+2),_alpha = RootOf(4*_Z^4-16*_Z^3+16*_Z^2-7*_Z+1))+11/571*Sum(_alpha^(-n+1),_alpha = RootOf(4*_Z^4-16*_Z^3+16*_Z^2-7*_Z+1))+50/571*Sum(_alpha^(-n),_alpha = RootOf(4*_Z^4-16*_Z^3+16*_Z^2-7*_Z+1))+1/571*Sum(_alpha^(-n-1),_alpha = RootOf(4*_Z^4-16*_Z^3+16*_Z^2-7*_Z+1))

Explicit closed form in latex syntax:
\frac{40 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(4 \textit{\_Z}^{4}-16 \textit{\_Z}^{3}+16 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{571}+\frac{11 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(4 \textit{\_Z}^{4}-16 \textit{\_Z}^{3}+16 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{571}+\frac{50 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(4 \textit{\_Z}^{4}-16 \textit{\_Z}^{3}+16 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{571}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(4 \textit{\_Z}^{4}-16 \textit{\_Z}^{3}+16 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{571}

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = -4*a(n)+16*a(n+1)-16*a(n+2)+7*a(n+3), n >= 4

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(n +4\right) = -4 a \! \left(n \right)+16 a \! \left(n +1\right)-16 a \! \left(n +2\right)+7 a \! \left(n +3\right), \quad n \geq 4

Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/14615/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[35,x]+F[7,x]+F[8,x]
F[7,x] = 0
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[15,x]
F[13,x] = F[14,x]
F[14,x] = F[11,x]+F[2,x]
F[15,x] = x
F[16,x] = F[17,x]+F[6,x]
F[17,x] = 2*F[7,x]+F[18,x]+F[22,x]
F[18,x] = F[15,x]*F[19,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = F[11,x]
F[21,x] = F[17,x]
F[22,x] = F[15,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[30,x]
F[25,x] = F[26,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[2,x]
F[29,x] = F[25,x]
F[30,x] = 2*F[7,x]+F[22,x]+F[31,x]
F[31,x] = F[15,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[11,x]
F[34,x] = F[30,x]
F[35,x] = F[15,x]*F[36,x]
F[36,x] = F[37,x]+F[5,x]
F[37,x] = F[25,x]+F[38,x]
F[38,x] = 2*F[7,x]+F[31,x]+F[39,x]
F[39,x] = F[15,x]*F[40,x]
F[40,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{6}\! \left(x \right)
F_{17}\! \left(x \right) = 2 F_{7}\! \left(x \right)+F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)
F_{30}\! \left(x \right) = 2 F_{7}\! \left(x \right)+F_{22}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{15}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{5}\! \left(x \right)
F_{37}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = 2 F_{7}\! \left(x \right)+F_{31}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_35(x) + F_7(x) + F_8(x))
Eq(F_7(x), 0)
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_15(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_11(x) + F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) + F_6(x))
Eq(F_17(x), F_18(x) + F_22(x) + 2*F_7(x))
Eq(F_18(x), F_15(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), F_11(x))
Eq(F_21(x), F_17(x))
Eq(F_22(x), F_15(x)*F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_30(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x), F_25(x))
Eq(F_30(x), F_22(x) + F_31(x) + 2*F_7(x))
Eq(F_31(x), F_15(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_11(x))
Eq(F_34(x), F_30(x))
Eq(F_35(x), F_15(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_5(x))
Eq(F_37(x), F_25(x) + F_38(x))
Eq(F_38(x), F_31(x) + F_39(x) + 2*F_7(x))
Eq(F_39(x), F_15(x)*F_40(x))
Eq(F_40(x), F_37(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [], "initial_strats": [{"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": "regular_insertion_encoding_left", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": 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[0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 3], [0, 3], [0, 0], [0, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"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, 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "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, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "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"}}, "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": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [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": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 2], [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": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "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", "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"}}]}

Specification 2
Strategy pack name: regular_insertion_encoding_right
Tree: http://permpal.com/tree/14616/
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[6,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[11,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = F[16,x]+F[7,x]
F[20,x] = F[16,x]
F[21,x] = F[22,x]+F[30,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[14,x]+F[25,x]
F[25,x] = F[22,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[25,x]+F[29,x]
F[29,x] = F[26,x]
F[30,x] = F[31,x]+F[32,x]+F[92,x]
F[31,x] = 0
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[56,x]
F[34,x] = F[35,x]+F[7,x]
F[35,x] = F[31,x]+F[36,x]+F[39,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[34,x]+F[38,x]
F[38,x] = F[16,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[10,x]+F[41,x]
F[41,x] = F[42,x]+F[49,x]
F[42,x] = F[31,x]+F[43,x]+F[46,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[11,x]+F[42,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[15,x]+F[48,x]
F[48,x] = F[42,x]
F[49,x] = 2*F[31,x]+F[50,x]+F[53,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[16,x]+F[49,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[20,x]+F[55,x]
F[55,x] = F[49,x]
F[56,x] = F[30,x]+F[57,x]
F[57,x] = 2*F[31,x]+F[58,x]+F[66,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[56,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[30,x]+F[61,x]
F[65,x] = F[61,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[26,x]+F[61,x]
F[69,x] = F[70,x]+F[81,x]
F[70,x] = 2*F[31,x]+F[71,x]+F[78,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[26,x]+F[74,x]
F[74,x] = 2*F[31,x]+F[71,x]+F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[29,x]+F[77,x]
F[77,x] = F[74,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[29,x]+F[80,x]
F[80,x] = F[70,x]
F[81,x] = 3*F[31,x]+F[82,x]+F[89,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[61,x]+F[85,x]
F[85,x] = 3*F[31,x]+F[82,x]+F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[65,x]+F[88,x]
F[88,x] = F[85,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[65,x]+F[91,x]
F[91,x] = F[81,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[21,x]+F[94,x]
F[94,x] = F[101,x]+F[95,x]
F[95,x] = F[31,x]+F[96,x]+F[98,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[45,x]+F[73,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[25,x]
F[100,x] = F[95,x]
F[101,x] = 2*F[31,x]+F[102,x]+F[112,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[108,x]
F[104,x] = F[105,x]+F[16,x]
F[105,x] = 2*F[31,x]+F[106,x]+F[53,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[104,x]
F[108,x] = F[109,x]+F[61,x]
F[109,x] = 3*F[31,x]+F[110,x]+F[86,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[108,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[64,x]
F[114,x] = F[101,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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right)+F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{92}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{56}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)+F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{31}\! \left(x \right)+F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{42}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right)+F_{49}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{20}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)
F_{56}\! \left(x \right) = F_{30}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{58}\! \left(x \right)+F_{66}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \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_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{30}\! \left(x \right)+F_{61}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{26}\! \left(x \right)+F_{61}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{81}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{71}\! \left(x \right)+F_{78}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{26}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{71}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{29}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{74}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{29}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{70}\! \left(x \right)
F_{81}\! \left(x \right) = 3 F_{31}\! \left(x \right)+F_{82}\! \left(x \right)+F_{89}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{61}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = 3 F_{31}\! \left(x \right)+F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{65}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{65}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{81}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{21}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{101}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{31}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{45}\! \left(x \right)+F_{73}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{25}\! \left(x \right)
F_{100}\! \left(x \right) = F_{95}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{102}\! \left(x \right)+F_{112}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{108}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{16}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{106}\! \left(x \right)+F_{53}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{104}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{61}\! \left(x \right)
F_{109}\! \left(x \right) = 3 F_{31}\! \left(x \right)+F_{110}\! \left(x \right)+F_{86}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{64}\! \left(x \right)
F_{114}\! \left(x \right) = F_{101}\! \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_6(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_11(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), F_16(x) + F_7(x))
Eq(F_20(x), F_16(x))
Eq(F_21(x), F_22(x) + F_30(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_14(x) + F_25(x))
Eq(F_25(x), F_22(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_25(x) + F_29(x))
Eq(F_29(x), F_26(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_92(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_56(x))
Eq(F_34(x), F_35(x) + F_7(x))
Eq(F_35(x), F_31(x) + F_36(x) + F_39(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_34(x) + F_38(x))
Eq(F_38(x), F_16(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_10(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_49(x))
Eq(F_42(x), F_31(x) + F_43(x) + F_46(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_11(x) + F_42(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_15(x) + F_48(x))
Eq(F_48(x), F_42(x))
Eq(F_49(x), 2*F_31(x) + F_50(x) + F_53(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_16(x) + F_49(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_20(x) + F_55(x))
Eq(F_55(x), F_49(x))
Eq(F_56(x), F_30(x) + F_57(x))
Eq(F_57(x), 2*F_31(x) + F_58(x) + F_66(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_56(x) + F_60(x))
Eq(F_60(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_64(x) + F_65(x))
Eq(F_64(x), F_30(x) + F_61(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_26(x) + F_61(x))
Eq(F_69(x), F_70(x) + F_81(x))
Eq(F_70(x), 2*F_31(x) + F_71(x) + F_78(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_26(x) + F_74(x))
Eq(F_74(x), 2*F_31(x) + F_71(x) + F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_29(x) + F_77(x))
Eq(F_77(x), F_74(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_29(x) + F_80(x))
Eq(F_80(x), F_70(x))
Eq(F_81(x), 3*F_31(x) + F_82(x) + F_89(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_61(x) + F_85(x))
Eq(F_85(x), 3*F_31(x) + F_82(x) + F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_65(x) + F_88(x))
Eq(F_88(x), F_85(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_65(x) + F_91(x))
Eq(F_91(x), F_81(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_21(x) + F_94(x))
Eq(F_94(x), F_101(x) + F_95(x))
Eq(F_95(x), F_31(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_45(x) + F_73(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_25(x))
Eq(F_100(x), F_95(x))
Eq(F_101(x), F_102(x) + F_112(x) + 2*F_31(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_108(x))
Eq(F_104(x), F_105(x) + F_16(x))
Eq(F_105(x), F_106(x) + 2*F_31(x) + F_53(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_104(x))
Eq(F_108(x), F_109(x) + F_61(x))
Eq(F_109(x), F_110(x) + 3*F_31(x) + F_86(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_108(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_64(x))
Eq(F_114(x), F_101(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [2], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [], "initial_strats": [{"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": "regular_insertion_encoding_right", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "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, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": 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{"patt": [3, 1, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[0, 4]]}]]}], "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, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 4], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 4], [0, 4], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 4], [0, 0], [0, 0], [0, 4]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 4], [0, 4], [0, 0], [0, 4]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 4]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 3]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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"}}]}

Specification 3
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14617/
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[6,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[11,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = F[16,x]+F[7,x]
F[20,x] = F[16,x]
F[21,x] = F[22,x]+F[30,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[14,x]+F[25,x]
F[25,x] = F[22,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[25,x]+F[29,x]
F[29,x] = F[26,x]
F[30,x] = F[31,x]+F[32,x]+F[92,x]
F[31,x] = 0
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[56,x]
F[34,x] = F[35,x]+F[7,x]
F[35,x] = F[31,x]+F[36,x]+F[39,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[34,x]+F[38,x]
F[38,x] = F[16,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[10,x]+F[41,x]
F[41,x] = F[42,x]+F[49,x]
F[42,x] = F[31,x]+F[43,x]+F[46,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[11,x]+F[42,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[15,x]+F[48,x]
F[48,x] = F[42,x]
F[49,x] = 2*F[31,x]+F[50,x]+F[53,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[16,x]+F[49,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[20,x]+F[55,x]
F[55,x] = F[49,x]
F[56,x] = F[30,x]+F[57,x]
F[57,x] = 2*F[31,x]+F[58,x]+F[66,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[56,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[30,x]+F[61,x]
F[65,x] = F[61,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[26,x]+F[61,x]
F[69,x] = F[70,x]+F[81,x]
F[70,x] = 2*F[31,x]+F[71,x]+F[78,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[26,x]+F[74,x]
F[74,x] = 2*F[31,x]+F[71,x]+F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[29,x]+F[77,x]
F[77,x] = F[74,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[29,x]+F[80,x]
F[80,x] = F[70,x]
F[81,x] = 3*F[31,x]+F[82,x]+F[89,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[61,x]+F[85,x]
F[85,x] = 3*F[31,x]+F[82,x]+F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[65,x]+F[88,x]
F[88,x] = F[85,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[65,x]+F[91,x]
F[91,x] = F[81,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[21,x]+F[94,x]
F[94,x] = F[101,x]+F[95,x]
F[95,x] = F[31,x]+F[96,x]+F[98,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[45,x]+F[73,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[25,x]
F[100,x] = F[95,x]
F[101,x] = 2*F[31,x]+F[102,x]+F[112,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[108,x]
F[104,x] = F[105,x]+F[16,x]
F[105,x] = 2*F[31,x]+F[106,x]+F[53,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[104,x]
F[108,x] = F[109,x]+F[61,x]
F[109,x] = 3*F[31,x]+F[110,x]+F[86,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[108,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[64,x]
F[114,x] = F[101,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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right)+F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{92}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{56}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)+F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{31}\! \left(x \right)+F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{42}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right)+F_{49}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{20}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)
F_{56}\! \left(x \right) = F_{30}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{58}\! \left(x \right)+F_{66}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \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_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{30}\! \left(x \right)+F_{61}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{26}\! \left(x \right)+F_{61}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{81}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{71}\! \left(x \right)+F_{78}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{26}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{71}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{29}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{74}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{29}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{70}\! \left(x \right)
F_{81}\! \left(x \right) = 3 F_{31}\! \left(x \right)+F_{82}\! \left(x \right)+F_{89}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{61}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = 3 F_{31}\! \left(x \right)+F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{65}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{65}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{81}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{21}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{101}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{31}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{45}\! \left(x \right)+F_{73}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{25}\! \left(x \right)
F_{100}\! \left(x \right) = F_{95}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{102}\! \left(x \right)+F_{112}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{108}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{16}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{106}\! \left(x \right)+F_{53}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{104}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{61}\! \left(x \right)
F_{109}\! \left(x \right) = 3 F_{31}\! \left(x \right)+F_{110}\! \left(x \right)+F_{86}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{64}\! \left(x \right)
F_{114}\! \left(x \right) = F_{101}\! \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_6(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_11(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), F_16(x) + F_7(x))
Eq(F_20(x), F_16(x))
Eq(F_21(x), F_22(x) + F_30(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_14(x) + F_25(x))
Eq(F_25(x), F_22(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_25(x) + F_29(x))
Eq(F_29(x), F_26(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_92(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_56(x))
Eq(F_34(x), F_35(x) + F_7(x))
Eq(F_35(x), F_31(x) + F_36(x) + F_39(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_34(x) + F_38(x))
Eq(F_38(x), F_16(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_10(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_49(x))
Eq(F_42(x), F_31(x) + F_43(x) + F_46(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_11(x) + F_42(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_15(x) + F_48(x))
Eq(F_48(x), F_42(x))
Eq(F_49(x), 2*F_31(x) + F_50(x) + F_53(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_16(x) + F_49(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_20(x) + F_55(x))
Eq(F_55(x), F_49(x))
Eq(F_56(x), F_30(x) + F_57(x))
Eq(F_57(x), 2*F_31(x) + F_58(x) + F_66(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_56(x) + F_60(x))
Eq(F_60(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_64(x) + F_65(x))
Eq(F_64(x), F_30(x) + F_61(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_26(x) + F_61(x))
Eq(F_69(x), F_70(x) + F_81(x))
Eq(F_70(x), 2*F_31(x) + F_71(x) + F_78(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_26(x) + F_74(x))
Eq(F_74(x), 2*F_31(x) + F_71(x) + F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_29(x) + F_77(x))
Eq(F_77(x), F_74(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_29(x) + F_80(x))
Eq(F_80(x), F_70(x))
Eq(F_81(x), 3*F_31(x) + F_82(x) + F_89(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_61(x) + F_85(x))
Eq(F_85(x), 3*F_31(x) + F_82(x) + F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_65(x) + F_88(x))
Eq(F_88(x), F_85(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_65(x) + F_91(x))
Eq(F_91(x), F_81(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_21(x) + F_94(x))
Eq(F_94(x), F_101(x) + F_95(x))
Eq(F_95(x), F_31(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_45(x) + F_73(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_25(x))
Eq(F_100(x), F_95(x))
Eq(F_101(x), F_102(x) + F_112(x) + 2*F_31(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_108(x))
Eq(F_104(x), F_105(x) + F_16(x))
Eq(F_105(x), F_106(x) + 2*F_31(x) + F_53(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_104(x))
Eq(F_108(x), F_109(x) + F_61(x))
Eq(F_109(x), F_110(x) + 3*F_31(x) + F_86(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_108(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_64(x))
Eq(F_114(x), F_101(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "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, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": 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