01342_02341_03241_10342_12340_13240_20341_21340
Counting sequence:
1, 1, 2, 6, 24, 112, 570, 3062, 17066, 97700, 570862, 3389812, 20394106, 124034760, 761292536, 4709264410, 29328534118, 183735748344, 1157070304524, 7320431897486, 46506419726168, 296557419720726, 1897451404446330, 12177717356311514, 78375302559831418, 505719712071758448, 3270914237978461438, 21202086645319360014, 137710953249161015952, 896141346003070435684, 5841802136842125821214, 38144258995681891996188, 249446890588493308120748, 1633625043009024548924276, 10713085597038669107251016, 70344555541153052654827672, 462454338496175668870204232, 3043694079490525249119321614, 20053978479375338306853334904, 132264468515800947864658344058, 873185455790511608795805137658, 5769918463811353750534660318186, 38160448752837691973102321282976, 252592228107029066056654331813832, 1673295125993202049495242742942852, 11093168883994131772851179947236494, 73596084978321679883758436284583454, 488603123036119562090272518056559198, 3245992357778103248702681269711146178, 21578266490369515066394289799991080056, 143533150272413703435036088922165333636, 955309184686320501030059429068392315634, 6361826810921850118595922070330486100554, 42389327952856956662417801804116005428634, 282591564192099318542769978015004280952042, 1884870367507711503681093944508151384375148, 12578113845957893303411157557117348018699720, 83975737169888873569330694920595363363747600, 560905005797791489686105371720119144373588388, 3748135434124628090824145289065299250885120378, 25056783606534258651339105627492535842889618406, 167576607147612644088792387430590365075653093492, 1121175809564769535581817099470147161261630886548, 7504137916896961337421070664215853087840123381732, 50244603723832292990945461671952535317307690406688, 336538367086694954164016307076337502056020732893464, 2254921975452174215487306653439300685296646115745774, 15113870119409785697860486324979703173819403753284370, 101335762084130598314306475917868289629864997117441982, 679655005783470701889748992086742858961462331561691344, 4559834239723083593858442544992941033132020928873914394, 30601346521737744660999029316875152514351017939399425430, 205427847672437393520881124875084253337555887768122989850, 1379437078822297286853050405617833129336700555668473525726, 9265415942682503037795386288275829936514692305921142503624, 62250833465498071281353812081918246822065263661453361410042, 418349787961675772979513626823802584560698439787389084912994, 2812192832409975637862359523489588735944867529170809634359718, 18908581295517937418333510653911749796973272495606292546479486, 127168148911899699674959671019887252873713590290655571972893334, 855461888618917582771808812365165922168759529394219091287678182, 5756033974495587762934492048657416866318440289199646898272060478, 38738602046616758848380451364147338979130978340198265652524687344, 260771478667033322716835202680167786167393709343335045718345957446, 1755777605624044717144075753091196440398507843779554439043254732928, 11824151716468238144189273823247087903972460569045500695527088690682, 79645167978979079592310071767458850792848105821853140500807094808736, 536581597994809725126800549239513281579012874740254446122374023823194, 3615738731560723994373282820972482839731473943502506380438928054433002, 24369202798128677177778011360121266186750199944991469888264471211895438, 164273219778874394510926328481909627335335019590452972273224720066161704, 1107571054383950982819444959111740983421204856602968793915455562593035496, 7468855851589500034590568110675595076444368173918629178755870837040963608, 50374707665894109061510157530791190566702883609842398162405462751450353542, 339817204153401674569540505592233892613948246130602493187040944821589352146, 2292719797589745171160248927133257706312153388114132737870065397003709760954, 15471338095901733128126242311521727080906215779300424929693087845292752551262, 104417809604708589912137920146160675732469099769669045270719426618401218907328, 704838568644347969710747999242666666749991295484841561804286093088556250450754, 4758518257470231561086742418202270468714455814781502642698172539232773280885486, 32130647364667724525722874174666415568807315225229966975148683112654491752667988
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24902/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[14,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[42,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[1,x]+F[18,x]+F[40,x]+F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[1,x]+F[26,x]+F[40,x]+F[41,x]+F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[15,x,k[0]]+F[38,x,k[0]]+F[39,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[14,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[14,x] = x
F[15,x,k[0]] = F[14,x]*F[16,x,k[0]]
F[16,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[17,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[18,x]+F[20,x,k[0]]+F[22,x,k[0]]
F[18,x] = F[14,x]*F[19,x]
F[19,x] = F[17,x,1]
F[20,x,k[0]] = F[17,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[14,x]*F[23,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[20,x,k[0]]+F[22,x,k[0]]+F[24,x,k[0]]+F[26,x]+F[29,x,k[0]]
F[24,x,k[0]] = F[14,x]*F[25,x,k[0]]
F[25,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[26,x] = F[14,x]*F[27,x]
F[27,x] = F[28,x,1]
F[28,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[29,x,k[0]] = F[14,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0],1]
F[31,x,k[0],k[1]] = (F[32,x,k[0],k[1]]*k[1]-F[32,x,k[0],1])/(-1+k[1])
F[32,x,k[0],k[1]] = F[1,x]+F[15,x,k[1]]+F[20,x,k[0]]+F[33,x,k[0],k[1]]+F[36,x,k[0],k[1]]+F[37,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[14,x]*F[34,x,k[0],k[1]]
F[34,x,k[0],k[1]] = 1/(-1+k[0])*(F[35,x,k[0],k[1]]*k[0]-F[35,x,1,k[1]])
F[35,x,k[0],k[1]] = (F[11,x,k[0]]*k[0]-F[11,x,k[1]]*k[1])/(-k[1]+k[0])
F[36,x,k[0],k[1]] = F[21,x,k[1]]*F[32,x,k[0],k[1]]
F[37,x,k[0],k[1]] = F[14,x]*F[31,x,k[0],k[1]]
F[38,x,k[0]] = F[11,x,k[0]]*F[21,x,k[0]]
F[39,x,k[0]] = F[10,x,k[0]]*F[14,x]
F[40,x] = F[14,x]*F[7,x]
F[41,x] = F[14,x]*F[9,x]
F[42,x] = F[14,x]*F[5,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_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)+F_{40}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{18}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y , 1\right)
F_{31}\! \left(x , y , z\right) = -\frac{-F_{32}\! \left(x , y , z\right) z +F_{32}\! \left(x , y , 1\right)}{-1+z}
F_{32}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , z\right)+F_{20}\! \left(x , y\right)+F_{33}\! \left(x , y , z\right)+F_{36}\! \left(x , y , z\right)+F_{37}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = F_{14}\! \left(x \right) F_{34}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = -\frac{-F_{35}\! \left(x , y , z\right) y +F_{35}\! \left(x , 1, z\right)}{-1+y}
F_{35}\! \left(x , y , z\right) = \frac{y F_{11}\! \left(x , y\right)-z F_{11}\! \left(x , z\right)}{-z +y}
F_{36}\! \left(x , y , z\right) = F_{21}\! \left(x , z\right) F_{32}\! \left(x , y , z\right)
F_{37}\! \left(x , y , z\right) = F_{14}\! \left(x \right) F_{31}\! \left(x , y , z\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \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_14(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_42(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_18(x) + F_40(x) + F_6(x))
Eq(F_6(x), F_14(x)*F_7(x))
Eq(F_7(x), F_1(x) + F_26(x) + F_40(x) + F_41(x) + F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), (-k_0*F_11(x, k_0) + F_11(x, 1))/(1 - k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_15(x, k_0) + F_38(x, k_0) + F_39(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_14(x))
Eq(F_13(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_14(x), x)
Eq(F_15(x, k_0), F_14(x)*F_16(x, k_0))
Eq(F_16(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_1(x) + F_12(x, k_0) + F_18(x) + F_20(x, k_0) + F_22(x, k_0))
Eq(F_18(x), F_14(x)*F_19(x))
Eq(F_19(x), F_17(x, 1))
Eq(F_20(x, k_0), F_17(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_14(x)*F_23(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_20(x, k_0) + F_22(x, k_0) + F_24(x, k_0) + F_26(x) + F_29(x, k_0))
Eq(F_24(x, k_0), F_14(x)*F_25(x, k_0))
Eq(F_25(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_26(x), F_14(x)*F_27(x))
Eq(F_27(x), F_28(x, 1))
Eq(F_28(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_29(x, k_0), F_14(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0, 1))
Eq(F_31(x, k_0, k_1), (-k_1*F_32(x, k_0, k_1) + F_32(x, k_0, 1))/(1 - k_1))
Eq(F_32(x, k_0, k_1), F_1(x) + F_15(x, k_1) + F_20(x, k_0) + F_33(x, k_0, k_1) + F_36(x, k_0, k_1) + F_37(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_14(x)*F_34(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), (k_0*F_35(x, k_0, k_1) - F_35(x, 1, k_1))/(k_0 - 1))
Eq(F_35(x, k_0, k_1), (-k_0*F_11(x, k_0) + k_1*F_11(x, k_1))/(-k_0 + k_1))
Eq(F_36(x, k_0, k_1), F_21(x, k_1)*F_32(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), F_14(x)*F_31(x, k_0, k_1))
Eq(F_38(x, k_0), F_11(x, k_0)*F_21(x, k_0))
Eq(F_39(x, k_0), F_10(x, k_0)*F_14(x))
Eq(F_40(x), F_14(x)*F_7(x))
Eq(F_41(x), F_14(x)*F_9(x))
Eq(F_42(x), F_14(x)*F_5(x))
Pack JSON:
{"name": "row_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 2
Strategy pack name: row_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25184/
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[5,x]
F[3,x] = F[1,x]+F[4,x]+F[74,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[1,x]+F[7,x]+F[70,x]+F[72,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[67,x,k[0]]+F[68,x,k[0]]+F[69,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[5,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[24,x,k[0]]+F[65,x,k[0]]+F[66,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[5,x]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[18,x,k[0]]+F[63,x,k[0]]+F[64,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[5,x]
F[17,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[18,x,k[0]] = F[19,x,k[0]]*F[5,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[20,x,k[0]]*k[0]-F[20,x,1])
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[29,x,k[0]]+F[61,x,k[0]]+F[62,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[5,x]
F[22,x,k[0]] = 1/(-1+k[0])*(F[23,x,k[0]]*k[0]-F[23,x,1])
F[23,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[24,x,k[0]]+F[25,x]+F[27,x,k[0]]
F[24,x,k[0]] = F[11,x,k[0]]*F[5,x]
F[25,x] = F[26,x]*F[5,x]
F[26,x] = F[23,x,1]
F[27,x,k[0]] = F[23,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = k[0]*x
F[29,x,k[0]] = F[30,x,k[0]]*F[5,x]
F[30,x,k[0]] = 1/(-1+k[0])*(F[31,x,k[0]]*k[0]-F[31,x,1])
F[31,x,k[0]] = F[32,x,k[0]]+F[6,x]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[28,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[42,x,k[0]]+F[6,x]+F[60,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[5,x]
F[36,x,k[0]] = F[37,x,k[0]]
F[38,x,k[0]] = F[37,x,k[0]]*F[5,x]
F[38,x,k[0]] = F[39,x,k[0]]
F[40,x,k[0]] = F[39,x,k[0]]+F[41,x,k[0]]
F[40,x,k[0]] = F[17,x,k[0]]
F[41,x,k[0]] = F[9,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]*F[5,x]*F[55,x]
F[43,x,k[0]] = F[44,x,k[0]]
F[45,x,k[0]] = F[44,x,k[0]]*F[5,x]
F[46,x,k[0]] = F[1,x]+F[45,x,k[0]]+F[53,x,k[0]]+F[54,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[47,x,k[0]]+F[49,x,k[0]]+F[51,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[23,x,k[0]]*F[5,x]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[31,x,k[0]]*F[5,x]
F[51,x,k[0]] = F[46,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = k[0]*x
F[53,x,k[0]] = F[8,x,k[0]]
F[54,x,k[0]] = F[46,x,k[0]]*F[52,x,k[0]]
F[55,x] = F[56,x,1]
F[56,x,k[0]] = F[1,x]+F[57,x,k[0]]+F[59,x,k[0]]
F[57,x,k[0]] = F[5,x]*F[58,x,k[0]]
F[58,x,k[0]] = 1/(-1+k[0])*(F[56,x,k[0]]*k[0]-F[56,x,1])
F[59,x,k[0]] = F[28,x,k[0]]*F[56,x,k[0]]
F[60,x,k[0]] = F[28,x,k[0]]*F[34,x,k[0]]
F[61,x,k[0]] = F[19,x,k[0]]*F[5,x]
F[62,x,k[0]] = F[20,x,k[0]]*F[28,x,k[0]]
F[63,x,k[0]] = F[30,x,k[0]]*F[5,x]
F[64,x,k[0]] = F[15,x,k[0]]*F[28,x,k[0]]
F[65,x,k[0]] = F[22,x,k[0]]*F[5,x]
F[66,x,k[0]] = F[12,x,k[0]]*F[28,x,k[0]]
F[67,x,k[0]] = F[14,x,k[0]]*F[5,x]
F[68,x,k[0]] = F[17,x,k[0]]*F[5,x]
F[69,x,k[0]] = F[28,x,k[0]]*F[9,x,k[0]]
F[70,x] = F[71,x,1]
F[71,x,k[0]] = F[20,x,k[0]]*F[5,x]
F[72,x] = F[5,x]*F[73,x]
F[73,x] = F[31,x,1]
F[74,x] = F[5,x]*F[75,x]
F[75,x] = F[1,x]+F[25,x]+F[76,x]+F[78,x]
F[76,x] = F[77,x,1]
F[77,x,k[0]] = F[15,x,k[0]]*F[5,x]
F[78,x] = F[79,x,1]
F[79,x,k[0]] = F[12,x,k[0]]*F[5,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_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{74}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-F_{12}\! \left(x , y\right) y +F_{12}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{65}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{14}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{17}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-F_{20}\! \left(x , y\right) y +F_{20}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{29}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{22}\! \left(x , y\right) = -\frac{-F_{23}\! \left(x , y\right) y +F_{23}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{25}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{5}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = y x
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{30}\! \left(x , y\right) = -\frac{-F_{31}\! \left(x , y\right) y +F_{31}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{42}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{60}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{5}\! \left(x \right) F_{55}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = y x
F_{53}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{55}\! \left(x \right) = F_{56}\! \left(x , 1\right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{57}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = -\frac{-y F_{56}\! \left(x , y\right)+F_{56}\! \left(x , 1\right)}{-1+y}
F_{59}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{64}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{66}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{68}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{69}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{70}\! \left(x \right) = F_{71}\! \left(x , 1\right)
F_{71}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{72}\! \left(x \right) = F_{5}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{31}\! \left(x , 1\right)
F_{74}\! \left(x \right) = F_{5}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x , 1\right)
F_{77}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x , 1\right)
F_{79}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{5}\! \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)*F_5(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_74(x))
Eq(F_4(x), F_5(x)*F_6(x))
Eq(F_5(x), x)
Eq(F_6(x), F_1(x) + F_7(x) + F_70(x) + F_72(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_67(x, k_0) + F_68(x, k_0) + F_69(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_5(x))
Eq(F_11(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_24(x, k_0) + F_65(x, k_0) + F_66(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_5(x))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0) + F_18(x, k_0) + F_63(x, k_0) + F_64(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_5(x))
Eq(F_17(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_18(x, k_0), F_19(x, k_0)*F_5(x))
Eq(F_19(x, k_0), (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_29(x, k_0) + F_61(x, k_0) + F_62(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_5(x))
Eq(F_22(x, k_0), (k_0*F_23(x, k_0) - F_23(x, 1))/(k_0 - 1))
Eq(F_23(x, k_0), F_1(x) + F_13(x, k_0) + F_24(x, k_0) + F_25(x) + F_27(x, k_0))
Eq(F_24(x, k_0), F_11(x, k_0)*F_5(x))
Eq(F_25(x), F_26(x)*F_5(x))
Eq(F_26(x), F_23(x, 1))
Eq(F_27(x, k_0), F_23(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), k_0*x)
Eq(F_29(x, k_0), F_30(x, k_0)*F_5(x))
Eq(F_30(x, k_0), (k_0*F_31(x, k_0) - F_31(x, 1))/(k_0 - 1))
Eq(F_31(x, k_0), F_32(x, k_0) + F_6(x))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_28(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_42(x, k_0) + F_6(x) + F_60(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_5(x))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_38(x, k_0), F_37(x, k_0)*F_5(x))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_40(x, k_0), F_39(x, k_0) + F_41(x, k_0))
Eq(F_40(x, k_0), F_17(x, k_0))
Eq(F_41(x, k_0), F_9(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0)*F_5(x)*F_55(x))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_45(x, k_0), F_44(x, k_0)*F_5(x))
Eq(F_46(x, k_0), F_1(x) + F_45(x, k_0) + F_53(x, k_0) + F_54(x, k_0))
Eq(F_46(x, k_0), F_1(x) + F_47(x, k_0) + F_49(x, k_0) + F_51(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_23(x, k_0)*F_5(x))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_31(x, k_0)*F_5(x))
Eq(F_51(x, k_0), F_46(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), k_0*x)
Eq(F_53(x, k_0), F_8(x, k_0))
Eq(F_54(x, k_0), F_46(x, k_0)*F_52(x, k_0))
Eq(F_55(x), F_56(x, 1))
Eq(F_56(x, k_0), F_1(x) + F_57(x, k_0) + F_59(x, k_0))
Eq(F_57(x, k_0), F_5(x)*F_58(x, k_0))
Eq(F_58(x, k_0), (k_0*F_56(x, k_0) - F_56(x, 1))/(k_0 - 1))
Eq(F_59(x, k_0), F_28(x, k_0)*F_56(x, k_0))
Eq(F_60(x, k_0), F_28(x, k_0)*F_34(x, k_0))
Eq(F_61(x, k_0), F_19(x, k_0)*F_5(x))
Eq(F_62(x, k_0), F_20(x, k_0)*F_28(x, k_0))
Eq(F_63(x, k_0), F_30(x, k_0)*F_5(x))
Eq(F_64(x, k_0), F_15(x, k_0)*F_28(x, k_0))
Eq(F_65(x, k_0), F_22(x, k_0)*F_5(x))
Eq(F_66(x, k_0), F_12(x, k_0)*F_28(x, k_0))
Eq(F_67(x, k_0), F_14(x, k_0)*F_5(x))
Eq(F_68(x, k_0), F_17(x, k_0)*F_5(x))
Eq(F_69(x, k_0), F_28(x, k_0)*F_9(x, k_0))
Eq(F_70(x), F_71(x, 1))
Eq(F_71(x, k_0), F_20(x, k_0)*F_5(x))
Eq(F_72(x), F_5(x)*F_73(x))
Eq(F_73(x), F_31(x, 1))
Eq(F_74(x), F_5(x)*F_75(x))
Eq(F_75(x), F_1(x) + F_25(x) + F_76(x) + F_78(x))
Eq(F_76(x), F_77(x, 1))
Eq(F_77(x, k_0), F_15(x, k_0)*F_5(x))
Eq(F_78(x), F_79(x, 1))
Eq(F_79(x, k_0), F_12(x, k_0)*F_5(x))
Pack JSON:
{"name": "row_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}, "children": [{"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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 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"SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 5]]}]}}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"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, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"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, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "ComponentToPointAssumptionStrategy", "ignore_parent": false, "inferrable": false, "possibly_empty": false, "workable": false, "assumption": {"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"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": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"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.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"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.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25222/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[14,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[42,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[1,x]+F[18,x]+F[40,x]+F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[1,x]+F[26,x]+F[40,x]+F[41,x]+F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[15,x,k[0]]+F[38,x,k[0]]+F[39,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[14,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[14,x] = x
F[15,x,k[0]] = F[14,x]*F[16,x,k[0]]
F[16,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[17,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[18,x]+F[20,x,k[0]]+F[22,x,k[0]]
F[18,x] = F[14,x]*F[19,x]
F[19,x] = F[17,x,1]
F[20,x,k[0]] = F[17,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[14,x]*F[23,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[20,x,k[0]]+F[22,x,k[0]]+F[24,x,k[0]]+F[26,x]+F[29,x,k[0]]
F[24,x,k[0]] = F[14,x]*F[25,x,k[0]]
F[25,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[26,x] = F[14,x]*F[27,x]
F[27,x] = F[28,x,1]
F[28,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[29,x,k[0]] = F[14,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0],1]
F[31,x,k[0],k[1]] = (F[32,x,k[0],k[1]]*k[1]-F[32,x,k[0],1])/(-1+k[1])
F[32,x,k[0],k[1]] = F[1,x]+F[15,x,k[1]]+F[20,x,k[0]]+F[33,x,k[0],k[1]]+F[36,x,k[0],k[1]]+F[37,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[14,x]*F[34,x,k[0],k[1]]
F[34,x,k[0],k[1]] = 1/(-1+k[0])*(F[35,x,k[0],k[1]]*k[0]-F[35,x,1,k[1]])
F[35,x,k[0],k[1]] = (F[11,x,k[0]]*k[0]-F[11,x,k[1]]*k[1])/(-k[1]+k[0])
F[36,x,k[0],k[1]] = F[21,x,k[1]]*F[32,x,k[0],k[1]]
F[37,x,k[0],k[1]] = F[14,x]*F[31,x,k[0],k[1]]
F[38,x,k[0]] = F[11,x,k[0]]*F[21,x,k[0]]
F[39,x,k[0]] = F[10,x,k[0]]*F[14,x]
F[40,x] = F[14,x]*F[7,x]
F[41,x] = F[14,x]*F[9,x]
F[42,x] = F[14,x]*F[5,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_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)+F_{40}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{18}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y , 1\right)
F_{31}\! \left(x , y , z\right) = -\frac{-F_{32}\! \left(x , y , z\right) z +F_{32}\! \left(x , y , 1\right)}{-1+z}
F_{32}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , z\right)+F_{20}\! \left(x , y\right)+F_{33}\! \left(x , y , z\right)+F_{36}\! \left(x , y , z\right)+F_{37}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = F_{14}\! \left(x \right) F_{34}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = -\frac{-F_{35}\! \left(x , y , z\right) y +F_{35}\! \left(x , 1, z\right)}{-1+y}
F_{35}\! \left(x , y , z\right) = \frac{y F_{11}\! \left(x , y\right)-z F_{11}\! \left(x , z\right)}{-z +y}
F_{36}\! \left(x , y , z\right) = F_{21}\! \left(x , z\right) F_{32}\! \left(x , y , z\right)
F_{37}\! \left(x , y , z\right) = F_{14}\! \left(x \right) F_{31}\! \left(x , y , z\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \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_14(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_42(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_18(x) + F_40(x) + F_6(x))
Eq(F_6(x), F_14(x)*F_7(x))
Eq(F_7(x), F_1(x) + F_26(x) + F_40(x) + F_41(x) + F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), (-k_0*F_11(x, k_0) + F_11(x, 1))/(1 - k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_15(x, k_0) + F_38(x, k_0) + F_39(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_14(x))
Eq(F_13(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_14(x), x)
Eq(F_15(x, k_0), F_14(x)*F_16(x, k_0))
Eq(F_16(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_1(x) + F_12(x, k_0) + F_18(x) + F_20(x, k_0) + F_22(x, k_0))
Eq(F_18(x), F_14(x)*F_19(x))
Eq(F_19(x), F_17(x, 1))
Eq(F_20(x, k_0), F_17(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_14(x)*F_23(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_20(x, k_0) + F_22(x, k_0) + F_24(x, k_0) + F_26(x) + F_29(x, k_0))
Eq(F_24(x, k_0), F_14(x)*F_25(x, k_0))
Eq(F_25(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_26(x), F_14(x)*F_27(x))
Eq(F_27(x), F_28(x, 1))
Eq(F_28(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_29(x, k_0), F_14(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0, 1))
Eq(F_31(x, k_0, k_1), (-k_1*F_32(x, k_0, k_1) + F_32(x, k_0, 1))/(1 - k_1))
Eq(F_32(x, k_0, k_1), F_1(x) + F_15(x, k_1) + F_20(x, k_0) + F_33(x, k_0, k_1) + F_36(x, k_0, k_1) + F_37(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_14(x)*F_34(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), (k_0*F_35(x, k_0, k_1) - F_35(x, 1, k_1))/(k_0 - 1))
Eq(F_35(x, k_0, k_1), (-k_0*F_11(x, k_0) + k_1*F_11(x, k_1))/(-k_0 + k_1))
Eq(F_36(x, k_0, k_1), F_21(x, k_1)*F_32(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), F_14(x)*F_31(x, k_0, k_1))
Eq(F_38(x, k_0), F_11(x, k_0)*F_21(x, k_0))
Eq(F_39(x, k_0), F_10(x, k_0)*F_14(x))
Eq(F_40(x), F_14(x)*F_7(x))
Eq(F_41(x), F_14(x)*F_9(x))
Eq(F_42(x), F_14(x)*F_5(x))
Pack JSON:
{"name": "row_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}], 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