0123_135024_145023_235014_245013_345012

Counting sequence:
1, 1, 2, 6, 23, 103, 508, 2656, 14381, 79533, 445638, 2517738, 14301411, 81529971, 465953088, 2667737988, 15293841113, 87765930841, 504055136842, 2896728015886, 16655920477871, 95813593245951, 551389144800452, 3174263519294056, 18279604502597893, 105297510195292933, 606718962427522958, 3496773540297994866, 20158186528602785403, 116234191345536441099, 670362966897150710664, 3867012338251741896204, 22311394955910344338353, 128753803701134269026993, 743143079657766239273874, 4290035905451770265845014, 24769819142546724304500039, 143039387251628466097317783, 826146324388013649490429068, 4772265581786192468836904304, 27571247569590822379321969629, 159312704850414620580912750429, 920671457593299934801947381078, 5321295877146349812433185983226, 30760037653105431844582954225683, 177832604728881944251746352812963, 1028227947252297535789839543979728, 5945924459356847981302448379377556, 34387443112663366631005517949382281, 198897580396649945669127395681723913, 1150553693890743909036824130518383578, 6656267538513620130885909027880674078, 38512338986339282082181948376423588831, 222850225142545812541065914812029756463, 1289641993705766202493413884844148568404, 7463921404147770744553627854158900065144, 43202182379481876144663461610714943049909, 250082916108060009493261564440296357772213, 1447775037348744852423487141744012393307678, 8382159280557305022758922911343686114356354, 48534166776388182030063193829238177700642219, 281044571728421590868600855941245481757826619, 1627563418496990577972331031840440759349529368, 9426162094302215559964999527982572750609643548, 54596568910872993763002480748227159600582831969, 316248507998127875805508266617185308963620156769, 1831991937488857717701159823846307725048102511394, 10613285417609903192419375792471740840692660907558, 61490304038643243862571349250052015995137029581431, 356281497614800214288073742726054989168021736769223, 2064472358467877729063402446302727326336430612192028, 11963366656650573619561410586011072398041060541987968, 69330714358531354121364649782548182230072724592101261, 401814180846443686772693468701270421456866776939767821, 2328904008185389414605722410498286589438791776310761958, 13499077753452126226414651602157296595008075439456210698, 78249621703696793175971457899481546166196634484364736323, 453613011349077978161257314842292497928721039337531957971, 2629743292558010476766064149368833941526372428875800297568, 15246329709438689803848137919686160107505367099731971905444, 88397681425593032642469658608885123508154908350771354916409, 512553952810613621773970886097435156162479752389247338277049, 2972083392012619306046043699608996154795688588622905150714218, 17234736291704649792918234274560405165100445645374822393452078, 99947080416301874061367181384802026173986831052474295395217679, 579638176859608610829675246554952025274006786843513841289901919, 3361745595540916129685368102631464563084717768781908773913590244, 19498145430148393849130240107944838013442900825852513329570988168, 113094628841356129243731397260868455917943778107341230654595356773, 656010051013851475413324139989100484019594619414802047915762797669, 3805383955420323140773642216503443803159981667162275240388702238894, 22075248100713577277077094221691563881041422566031700829783520373394, 128065302621925109554829109024383552358230578557800000953305043313883, 742977748784289354234101386117564477305936812341636184817533943810411, 4310605196244745112709303742000304703757496928438613952982449778501288, 25010275952131024562287907628119623066223389735653571803775367956647468, 145116302202019483286240113936093493501159208442972847027771308541545233, 842036863438534290404454656574624577058650701986775025654781008456935441, 4886106099046706610485152329505772919067766165445435882231379299962085042, 28353800603212510358223986289807681181056557043729790074075783256623551286, 164541702846517233687596452222545137509549847241666234786778551654629089191

Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24085/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[22,x]+F[4,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,1,k[0]]
F[7,x,k[0],k[1]] = F[8,x,k[0]*k[1],k[1]]
F[8,x,k[0],k[1]] = F[1,x]+F[17,x,k[0],k[1]]+F[19,x,k[0],k[1]]+F[9,x,k[0],k[1]]
F[9,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[13,x,k[0]]
F[10,x,k[0],k[1]] = (F[11,x,k[0],k[1]]*k[1]-F[11,x,k[0],1])/(-1+k[1])
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[13,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0],k[1]] = F[13,x,k[1]]*F[15,x,k[0],k[1]]
F[15,x,k[0],k[1]] = (-F[16,x,1,k[1]]*k[1]+F[16,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[16,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[17,x,k[0],k[1]] = F[13,x,k[1]]*F[18,x,k[0],k[1]]
F[18,x,k[0],k[1]] = (-F[7,x,1,k[1]]*k[1]+F[7,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[21,x]
F[20,x,k[0],k[1]] = (F[8,x,k[0],k[1]]*k[1]-F[8,x,k[0],1])/(-1+k[1])
F[21,x] = x
F[22,x] = F[21,x]*F[23,x]
F[23,x] = F[24,x,1]
F[24,x,k[0]] = (F[25,x,k[0]]*k[0]-F[25,x,1])/(-1+k[0])
F[25,x,k[0]] = F[1,x]+F[26,x,k[0]]+F[27,x,k[0]]
F[26,x,k[0]] = F[13,x,k[0]]*F[6,x,k[0]]
F[27,x,k[0]] = F[21,x]*F[24,x,k[0]]
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_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , 1, y\right)
F_{7}\! \left(x , y , z\right) = F_{8}\! \left(x , y z , z\right)
F_{8}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , y , z\right)+F_{9}\! \left(x , y , z\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y , z\right) F_{13}\! \left(x , y\right)
F_{10}\! \left(x , y , z\right) = \frac{z F_{11}\! \left(x , y , z\right)-F_{11}\! \left(x , y , 1\right)}{-1+z}
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)
F_{12}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{15}\! \left(x , y , z\right)
F_{15}\! \left(x , y , z\right) = \frac{-z F_{16}\! \left(x , 1, z\right)+y F_{16}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{16}\! \left(x , y , z\right) = F_{11}\! \left(x , y z , z\right)
F_{17}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{18}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = \frac{-z F_{7}\! \left(x , 1, z\right)+y F_{7}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , y , z\right) F_{21}\! \left(x \right)
F_{20}\! \left(x , y , z\right) = \frac{z F_{8}\! \left(x , y , z\right)-F_{8}\! \left(x , y , 1\right)}{-1+z}
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{24}\! \left(x , y\right) = \frac{y F_{25}\! \left(x , y\right)-F_{25}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\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_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_22(x) + F_4(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, 1, k_0))
Eq(F_7(x, k_0, k_1), F_8(x, k_0*k_1, k_1))
Eq(F_8(x, k_0, k_1), F_1(x) + F_17(x, k_0, k_1) + F_19(x, k_0, k_1) + F_9(x, k_0, k_1))
Eq(F_9(x, k_0, k_1), F_10(x, k_0, k_1)*F_13(x, k_0))
Eq(F_10(x, k_0, k_1), (-k_1*F_11(x, k_0, k_1) + F_11(x, k_0, 1))/(1 - k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_11(x, k_0, k_1)*F_13(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0, k_1), F_13(x, k_1)*F_15(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), (-k_0*F_16(x, k_0/k_1, k_1) + k_1*F_16(x, 1, k_1))/(-k_0 + k_1))
Eq(F_16(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_17(x, k_0, k_1), F_13(x, k_1)*F_18(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), (-k_0*F_7(x, k_0/k_1, k_1) + k_1*F_7(x, 1, k_1))/(-k_0 + k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_21(x))
Eq(F_20(x, k_0, k_1), (-k_1*F_8(x, k_0, k_1) + F_8(x, k_0, 1))/(1 - k_1))
Eq(F_21(x), x)
Eq(F_22(x), F_21(x)*F_23(x))
Eq(F_23(x), F_24(x, 1))
Eq(F_24(x, k_0), (-k_0*F_25(x, k_0) + F_25(x, 1))/(1 - k_0))
Eq(F_25(x, k_0), F_1(x) + F_26(x, k_0) + F_27(x, k_0))
Eq(F_26(x, k_0), F_13(x, k_0)*F_6(x, k_0))
Eq(F_27(x, k_0), F_21(x)*F_24(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "row_and_col_placements_tracked_fusion_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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 5, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 5, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 5, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 5, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 0, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 5, 0, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 5, 0, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 5, 0, 2, 3], 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[[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [0, 2]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 1], [0, 3]], [[1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 0, "strategy_class": "FusionStrategy", "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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"}}]}

Specification 2
Strategy pack name: point_and_row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/24086/
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[22,x]*F[4,x]
F[4,x] = F[1,x]+F[23,x]+F[5,x]
F[5,x] = F[22,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[8,x,1,k[0]]
F[8,x,k[0],k[1]] = F[9,x,k[0]*k[1],k[1]]
F[9,x,k[0],k[1]] = F[1,x]+F[10,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[20,x,k[0],k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[14,x,k[0]]
F[11,x,k[0],k[1]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],1])/(-1+k[1])
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0],k[1]] = F[14,x,k[1]]*F[16,x,k[0],k[1]]
F[16,x,k[0],k[1]] = (-F[17,x,1,k[1]]*k[1]+F[17,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[17,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[18,x,k[0],k[1]] = F[14,x,k[1]]*F[19,x,k[0],k[1]]
F[19,x,k[0],k[1]] = (-F[8,x,1,k[1]]*k[1]+F[8,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[22,x]
F[21,x,k[0],k[1]] = (F[9,x,k[0],k[1]]*k[1]-F[9,x,k[0],1])/(-1+k[1])
F[22,x] = x
F[23,x] = F[22,x]*F[24,x]
F[24,x] = F[25,x,1]
F[25,x,k[0]] = (F[26,x,k[0]]*k[0]-F[26,x,1])/(-1+k[0])
F[26,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[28,x,k[0]]
F[27,x,k[0]] = F[14,x,k[0]]*F[7,x,k[0]]
F[28,x,k[0]] = F[22,x]*F[25,x,k[0]]
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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{22}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , 1, y\right)
F_{8}\! \left(x , y , z\right) = F_{9}\! \left(x , y z , z\right)
F_{9}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right) F_{14}\! \left(x , y\right)
F_{11}\! \left(x , y , z\right) = -\frac{-z F_{12}\! \left(x , y , z\right)+F_{12}\! \left(x , y , 1\right)}{-1+z}
F_{12}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)
F_{13}\! \left(x , y , z\right) = F_{12}\! \left(x , y , z\right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{16}\! \left(x , y , z\right)
F_{16}\! \left(x , y , z\right) = -\frac{z F_{17}\! \left(x , 1, z\right)-y F_{17}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{17}\! \left(x , y , z\right) = F_{12}\! \left(x , y z , z\right)
F_{18}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)
F_{19}\! \left(x , y , z\right) = -\frac{z F_{8}\! \left(x , 1, z\right)-y F_{8}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{20}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right) F_{22}\! \left(x \right)
F_{21}\! \left(x , y , z\right) = -\frac{-z F_{9}\! \left(x , y , z\right)+F_{9}\! \left(x , y , 1\right)}{-1+z}
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{22}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{25}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{25}\! \left(x , y\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_22(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_23(x) + F_5(x))
Eq(F_5(x), F_22(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_8(x, 1, k_0))
Eq(F_8(x, k_0, k_1), F_9(x, k_0*k_1, k_1))
Eq(F_9(x, k_0, k_1), F_1(x) + F_10(x, k_0, k_1) + F_18(x, k_0, k_1) + F_20(x, k_0, k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0, k_1)*F_14(x, k_0))
Eq(F_11(x, k_0, k_1), (-k_1*F_12(x, k_0, k_1) + F_12(x, k_0, 1))/(1 - k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_12(x, k_0, k_1)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0, k_1), F_14(x, k_1)*F_16(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0/k_1, k_1) + k_1*F_17(x, 1, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_18(x, k_0, k_1), F_14(x, k_1)*F_19(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), (-k_0*F_8(x, k_0/k_1, k_1) + k_1*F_8(x, 1, k_1))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1)*F_22(x))
Eq(F_21(x, k_0, k_1), (-k_1*F_9(x, k_0, k_1) + F_9(x, k_0, 1))/(1 - k_1))
Eq(F_22(x), x)
Eq(F_23(x), F_22(x)*F_24(x))
Eq(F_24(x), F_25(x, 1))
Eq(F_25(x, k_0), (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))
Eq(F_26(x, k_0), F_1(x) + F_27(x, k_0) + F_28(x, k_0))
Eq(F_27(x, k_0), F_14(x, k_0)*F_7(x, k_0))
Eq(F_28(x, k_0), F_22(x)*F_25(x, k_0))
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"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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"pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 3], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 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