0132_0321_1032

Counting sequence:
1, 1, 2, 6, 21, 79, 313, 1290, 5475, 23764, 105001, 470738, 2136022, 9791501, 45275765, 210931962, 989153896, 4665405537, 22117490066, 105333232395, 503705307121, 2417668815331, 11643343605157, 56245830951016, 272472137759191, 1323348118582689, 6442568004611628, 31433974955871460, 153683012533869425, 752795159251628052, 3693997001327533190, 18156613448026993444, 89381228632011197346, 440645870613532706588, 2175341407212566957350, 10752889057998062826881, 53217134591781509581218, 263680207740700138287741, 1307906629571308349273533, 6494184393897040442337847, 32277397575592155550529754, 160574824679469784590702342, 799543300553407453895585912, 3984501693885002714711293201, 19872691447630648418078507871, 99191462551669067261477655977, 495464047243014059321034637613, 2476603642721374238446691170020, 12387809132311973074016513291560, 62003193795689752215287645791709, 310530186994057276074785807304451, 1556155963769015542924303121448323, 7802825500187653964686764353225547, 39146294733223144321629416402748196, 196499056842860327334776085864271114, 986853895587572665576618778904145974, 4958608565057163327582319772396273394, 24927216701807984116765286876596217439, 125368249857542763602787663774137920777, 630803842651925258857088721732861981894, 3175320854316724309964774912393915448430, 15990471330416462892014356683418620737000, 80558138771958189796036236538566872854166, 406000452068197737123956756416446713179488, 2046949998489373385838522539834997932886083, 10323964672954293740560892678996827660280433, 52088219300712600481127983081396665144337939, 262894573370311088196596130170241428095077860, 1327297973166966005490086920698287705441631145, 6703409055911440579252762982815084680628691069, 33865653219952620074739163229453286675536478639, 171141672558798419928614204390834253397949941823, 865129186920652587705721889660469915774900818722, 4374530846625898777495235413426396974303663775101, 22126051775890360355808648027344941894146609072985, 111942504434241314024921588328714244848514870844357, 566502236097259476741101292365109312028199929771931, 2867614297965733909311893635253517854333717906307927, 14519425937205451745339016730541020200195854516271741, 73533453960043553759477819680275344833023597161540411, 372498573407757059445191510551503155967174877715162194, 1887408063744173491154281452966040946301954399310556963, 9565464279883760612825524066462298505183450035730690510, 48488970094304924878417347399923284108356181265512123565, 245852263208405401555213291256881929986199403982087051134, 1246802247157922141779309127111028682961151867558860050941, 6324277313329316529923753106055744851285774939986236692113, 32085744374061830774012539875556594998208049696944375251337, 162816799027258348513855494979708373515540901385284468436446, 826361824635999446010785264388585222156886299595878843105150, 4194916750217858920524933399795822084499155100647773099279682, 21298876852383995552395223948474794286650929571107259627648281, 108160468989739679375568014145275410406787255727907825378934537, 549360245774993081663682627084008814062476505357805011884093371, 2790750827987999543599257750340160454690511714153848860504873495, 14179420219222601845390617010026845000149012129578717234292811416, 72055630525624918503453489062656182802637008062895966422765150141, 366224942253930068241630056122255032387255735897732005328999277357, 1861645637104265575724273627213222691819436599570839130306253712106, 9464851714281648765952390329806262881421343636632089760525638666470, 48127904409211104914797320006011459120402612498016737950982389946111

Implicit equation for the generating function in Maple syntax:
(2*x+1)*x*F(x)^4+(x^2-7*x-1)*F(x)^3+(-x^2+7*x+6)*F(x)^2-10*F(x)+5 = 0

Implicit equation for the generating function in latex syntax:
\left(2 x +1\right) x F \! \left(x \right)^{4}+\left(x^{2}-7 x -1\right) F \! \left(x \right)^{3}+\left(-x^{2}+7 x +6\right) F \! \left(x \right)^{2}-10 F \! \left(x \right)+5 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 79
a(6) = 313
a(7) = 1290
a(8) = 5475
a(9) = 23764
a(10) = 105001
a(11) = 470738
a(12) = 2136022
a(n+13) = -16*n*(n+1)*(n+2)/(n+14)/(n+13)/(n+12)*a(n)+2*(237*n+628)*(n+2)*(n+1)/(n+14)/(n+13)/(n+12)*a(n+1)-(n+2)*(4075*n^2+26467*n+41536)/(n+14)/(n+13)/(n+12)*a(n+2)+2*(4211*n^3+52076*n^2+204311*n+257406)/(n+14)/(n+13)/(n+12)*a(n+3)-2*(3064*n^3+50253*n^2+259334*n+426528)/(n+14)/(n+13)/(n+12)*a(n+4)+(4417*n^3+90167*n^2+575174*n+1166476)/(n+14)/(n+13)/(n+12)*a(n+5)-(841*n^3+31655*n^2+291840*n+787068)/(n+14)/(n+13)/(n+12)*a(n+6)-2*(98*n^3-2161*n^2-45572*n-177626)/(n+14)/(n+13)/(n+12)*a(n+7)+2*(158*n^3+1589*n^2-6352*n-71226)/(n+14)/(n+13)/(n+12)*a(n+8)-3*(75*n^3+1597*n^2+10040*n+15672)/(n+14)/(n+13)/(n+12)*a(n+9)+(49*n^3+1147*n^2+7670*n+10844)/(n+14)/(n+13)/(n+12)*a(n+10)-2*(14*n^2+275*n+1310)/(n+13)/(n+14)*a(n+11)+10*(n+11)/(n+14)*a(n+12), n >= 13

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) = 21
a \! \left(5\right) = 79
a \! \left(6\right) = 313
a \! \left(7\right) = 1290
a \! \left(8\right) = 5475
a \! \left(9\right) = 23764
a \! \left(10\right) = 105001
a \! \left(11\right) = 470738
a \! \left(12\right) = 2136022
a \! \left(n +13\right) = -\frac{16 n \left(n +1\right) \left(n +2\right) a \! \left(n \right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}+\frac{2 \left(237 n +628\right) \left(n +2\right) \left(n +1\right) a \! \left(n +1\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}-\frac{\left(n +2\right) \left(4075 n^{2}+26467 n +41536\right) a \! \left(n +2\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}+\frac{2 \left(4211 n^{3}+52076 n^{2}+204311 n +257406\right) a \! \left(n +3\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}-\frac{2 \left(3064 n^{3}+50253 n^{2}+259334 n +426528\right) a \! \left(n +4\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}+\frac{\left(4417 n^{3}+90167 n^{2}+575174 n +1166476\right) a \! \left(n +5\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}-\frac{\left(841 n^{3}+31655 n^{2}+291840 n +787068\right) a \! \left(n +6\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}-\frac{2 \left(98 n^{3}-2161 n^{2}-45572 n -177626\right) a \! \left(n +7\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}+\frac{2 \left(158 n^{3}+1589 n^{2}-6352 n -71226\right) a \! \left(n +8\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}-\frac{3 \left(75 n^{3}+1597 n^{2}+10040 n +15672\right) a \! \left(n +9\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}+\frac{\left(49 n^{3}+1147 n^{2}+7670 n +10844\right) a \! \left(n +10\right)}{\left(n +14\right) \left(n +13\right) \left(n +12\right)}-\frac{2 \left(14 n^{2}+275 n +1310\right) a \! \left(n +11\right)}{\left(n +13\right) \left(n +14\right)}+\frac{10 \left(n +11\right) a \! \left(n +12\right)}{n +14}, \quad n \geq 13

Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/275/
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[12,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[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = 1/F[12,x]*F[11,x]
F[11,x] = F[2,x]
F[12,x] = x
F[13,x] = F[14,x]*F[27,x]
F[14,x] = F[0,x]+F[15,x]
F[15,x] = 1/F[26,x]*F[16,x]
F[16,x] = -F[23,x]+F[17,x]
F[17,x] = 1/F[12,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[2,x]+F[20,x]
F[20,x] = -F[0,x]+F[21,x]
F[21,x] = 1/F[12,x]*F[22,x]
F[22,x] = F[2,x]
F[23,x] = F[2,x]*F[24,x]
F[24,x] = 1/F[12,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = F[0,x]+F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[1,x]+F[28,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[2,x]+F[31,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[2,x]*F[30,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[10,x]*F[34,x]
F[41,x] = F[14,x]*F[42,x]
F[42,x] = -F[46,x]+F[43,x]
F[43,x] = 1/F[12,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = -F[0,x]+F[24,x]
F[46,x] = F[26,x]+F[35,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_{12}\! \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_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{27}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)
F_{23}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right) F_{34}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{46}\! \left(x \right) = F_{26}\! \left(x \right)+F_{35}\! \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_12(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_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x)/F_12(x))
Eq(F_11(x), F_2(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x)*F_27(x))
Eq(F_14(x), F_0(x) + F_15(x))
Eq(F_15(x), F_16(x)/F_26(x))
Eq(F_16(x), F_17(x) - F_23(x))
Eq(F_17(x), F_18(x)/F_12(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_2(x) + F_20(x))
Eq(F_20(x), -F_0(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_12(x))
Eq(F_22(x), F_2(x))
Eq(F_23(x), F_2(x)*F_24(x))
Eq(F_24(x), F_25(x)/F_12(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), F_0(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_1(x) + F_28(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_2(x) + F_31(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_2(x)*F_30(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_10(x)*F_34(x))
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_43(x) - F_46(x))
Eq(F_43(x), F_44(x)/F_12(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), -F_0(x) + F_24(x))
Eq(F_46(x), F_26(x) + F_35(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}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_placements_req_corrob", "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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], 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"rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}]}

Specification 2
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/276/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[81,x]+F[9,x]
F[9,x] = F[10,x]+F[76,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[14,x]
F[13,x] = x
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x]
F[17,x] = F[13,x]*F[18,x]
F[18,x] = F[15,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = F[14,x]*F[2,x]
F[21,x] = F[22,x]+F[6,x]
F[22,x] = F[23,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[53,x]
F[25,x] = F[26,x]+F[48,x]
F[26,x] = F[27,x]+F[34,x]
F[27,x] = F[28,x]+F[29,x]+F[32,x]
F[28,x] = 0
F[29,x] = F[13,x]*F[30,x]
F[30,x] = F[11,x]+F[31,x]
F[31,x] = F[29,x]
F[32,x] = F[13,x]*F[33,x]
F[33,x] = F[11,x]+F[27,x]
F[34,x] = F[16,x]+F[35,x]
F[35,x] = -F[16,x]+F[36,x]
F[36,x] = -F[15,x]+F[37,x]
F[37,x] = -F[19,x]+F[38,x]
F[38,x] = 1/F[13,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[2,x]+F[41,x]
F[41,x] = -F[44,x]+F[42,x]
F[42,x] = 1/F[13,x]*F[43,x]
F[43,x] = F[2,x]
F[44,x] = F[1,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[13,x]*F[47,x]
F[47,x] = F[14,x]+F[33,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[11,x]*F[27,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[16,x]*F[45,x]
F[52,x] = F[11,x]*F[35,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[2,x]*F[26,x]
F[55,x] = F[56,x]+F[69,x]
F[56,x] = F[27,x]*F[57,x]
F[57,x] = 1/F[67,x]*F[58,x]
F[58,x] = -F[68,x]+F[59,x]
F[59,x] = -F[66,x]+F[60,x]
F[60,x] = 1/F[13,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = -F[2,x]+F[63,x]
F[63,x] = -F[0,x]+F[64,x]
F[64,x] = 1/F[13,x]*F[65,x]
F[65,x] = F[2,x]
F[66,x] = F[11,x]*F[67,x]
F[67,x] = F[14,x]+F[15,x]
F[68,x] = F[2,x]*F[42,x]
F[69,x] = F[70,x]+F[75,x]
F[70,x] = F[16,x]*F[71,x]
F[71,x] = -F[2,x]+F[72,x]
F[72,x] = -F[44,x]+F[73,x]
F[73,x] = 1/F[13,x]*F[74,x]
F[74,x] = F[2,x]
F[75,x] = F[35,x]*F[57,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[11,x]^2
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[2,x]*F[45,x]
F[80,x] = F[11,x]*F[16,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[10,x]*F[2,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[11,x]*F[57,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[2,x]*F[71,x]
F[87,x] = F[16,x]*F[57,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{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_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{81}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{76}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \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_{17}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \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_{14}\! \left(x \right) F_{2}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{6}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{53}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{48}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{13}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{13}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{15}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{19}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right)+F_{33}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{16}\! \left(x \right) F_{45}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right) F_{35}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{69}\! \left(x \right)
F_{56}\! \left(x \right) = F_{27}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = \frac{F_{58}\! \left(x \right)}{F_{67}\! \left(x \right)}
F_{58}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{65}\! \left(x \right) = F_{2}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{68}\! \left(x \right) = F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
F_{70}\! \left(x \right) = F_{16}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{2}\! \left(x \right)
F_{75}\! \left(x \right) = F_{35}\! \left(x \right) F_{57}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11} \left(x \right)^{2}
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{2}\! \left(x \right) F_{45}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{2}\! \left(x \right) F_{71}\! \left(x \right)
F_{87}\! \left(x \right) = F_{16}\! \left(x \right) F_{57}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_81(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_76(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_14(x))
Eq(F_13(x), x)
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_13(x)*F_18(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_14(x)*F_2(x))
Eq(F_21(x), F_22(x) + F_6(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_13(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_53(x))
Eq(F_25(x), F_26(x) + F_48(x))
Eq(F_26(x), F_27(x) + F_34(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_32(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_13(x)*F_30(x))
Eq(F_30(x), F_11(x) + F_31(x))
Eq(F_31(x), F_29(x))
Eq(F_32(x), F_13(x)*F_33(x))
Eq(F_33(x), F_11(x) + F_27(x))
Eq(F_34(x), F_16(x) + F_35(x))
Eq(F_35(x), -F_16(x) + F_36(x))
Eq(F_36(x), -F_15(x) + F_37(x))
Eq(F_37(x), -F_19(x) + F_38(x))
Eq(F_38(x), F_39(x)/F_13(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), -F_2(x) + F_41(x))
Eq(F_41(x), F_42(x) - F_44(x))
Eq(F_42(x), F_43(x)/F_13(x))
Eq(F_43(x), F_2(x))
Eq(F_44(x), F_1(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_13(x)*F_47(x))
Eq(F_47(x), F_14(x) + F_33(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_11(x)*F_27(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_16(x)*F_45(x))
Eq(F_52(x), F_11(x)*F_35(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_2(x)*F_26(x))
Eq(F_55(x), F_56(x) + F_69(x))
Eq(F_56(x), F_27(x)*F_57(x))
Eq(F_57(x), F_58(x)/F_67(x))
Eq(F_58(x), F_59(x) - F_68(x))
Eq(F_59(x), F_60(x) - F_66(x))
Eq(F_60(x), F_61(x)/F_13(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), -F_2(x) + F_63(x))
Eq(F_63(x), -F_0(x) + F_64(x))
Eq(F_64(x), F_65(x)/F_13(x))
Eq(F_65(x), F_2(x))
Eq(F_66(x), F_11(x)*F_67(x))
Eq(F_67(x), F_14(x) + F_15(x))
Eq(F_68(x), F_2(x)*F_42(x))
Eq(F_69(x), F_70(x) + F_75(x))
Eq(F_70(x), F_16(x)*F_71(x))
Eq(F_71(x), -F_2(x) + F_72(x))
Eq(F_72(x), -F_44(x) + F_73(x))
Eq(F_73(x), F_74(x)/F_13(x))
Eq(F_74(x), F_2(x))
Eq(F_75(x), F_35(x)*F_57(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_11(x)**2)
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_2(x)*F_45(x))
Eq(F_80(x), F_11(x)*F_16(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_10(x)*F_2(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_11(x)*F_57(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_2(x)*F_71(x))
Eq(F_87(x), F_16(x)*F_57(x))
Pack JSON:
{"expansion_strats": [[{"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}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_placements", "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:
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[0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"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": [], 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{"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 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, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": 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