0123_0231_0312

Counting sequence:
1, 1, 2, 6, 21, 79, 310, 1251, 5151, 21536, 91137, 389510, 1678565, 7284975, 31811311, 139661231, 616097345, 2729518734, 12139620771, 54181709667, 242603277963, 1089487427660, 4906014417063, 22147650846291, 100216641145675, 454459064260660, 2065042593916742, 9401243324422881, 42875744357878842, 195866829629921243, 896168786052340513, 4106378057645706969, 18842216287469029209, 86571632542075561372, 398252971818839729701, 1834230031710111704233, 8457336309060333783177, 39036781751389787223870, 180365025909020114710318, 834156339529680276717847, 3861354829006518592202775, 17890016475767651524211318, 82955156182847110029391309, 384965308565262186036340741, 1787846920003150484964427703, 8309128774814217256594245696, 38644156102086331768145299556, 179846874475675644868684719419, 837531160480072714376285471173, 3902716710462484596977339900742, 18196616727608809539718967388116, 84891070023465093054011674929698, 396252325798051432595523729485340, 1850594713750955192982517073668076, 8647133724163890140115080795308801, 40424673740532914469613381396895880, 189071859222296553057698973868318356, 884720727574834524846856239509450608, 4141691188878143783837951626626597144, 19397020791940170510776031380569840111, 90880784266421477975044518154476753496, 425973931901781545451940501306479569323, 1997387733206820048729746707881668129871, 9369250876917388274411663089225256177013, 43964837047727968079984769881370085165317, 206376090421184024427002071455430194905412, 969085341568536369929425944689226461523325, 4552070890569644800382561100030529857331503, 21389280030796086049430585496486883475556357, 100535504247806731415207493746197048825025264, 472688521238110709903982009834722497663300256, 2223101385887048675499716309948923387279715605, 10458479956280682005756840919678898543323689901, 49215235076962624604227572203147236681731511372, 231658906530356443915445868691507831502814008584, 1090721208363775336039562062251991757174760949898, 5136778362544282932548639886227128607045891832384, 24197880264794537363559740838030277282270257823474, 114017225135275946888186832149802778161300418840390, 537362783787320614241047500832675145710620095102499, 2533180301945978033246499751954032894102090430904667, 11944377981352221303828355533155637016851143519238098, 56332302443148553535425394956714299475546706247037377, 265733121628425401968083448441793823699507199123664951, 1253793100306148685645698427067777146909595569631689611, 5916922965212061851411610687429920458386577803719745534, 27928893884914032587515694053041503585929146989234278744, 131855222859059661357537896954919048972821934302323946447, 622622462909988910334666320788585947828950363306955678915, 2940588204592176849304860044043134042151079731840024048868, 13890689617148503697030354182781585666390490698256521726592, 65628401472544653169731254424058750707089478723212594357604, 310124856225476893359611187010858473447422625990938897329660, 1465738242169029600479956196290423051531967546302590220945220, 6928668287313512366792790284953155781435806821417290311122178, 32757827542332980092176920531588710430089449188492731918324629, 154899814526137829141758400485537436070260711255868494443932533, 732581156882844773982593113328401137748184687408614860694622588, 3465199405891063029970991385368011801610255665387984963587168526, 16393323283387799660691525930127439965283344620947030297502141468, 77565883533923975381211004729200332643592833424364684410083412402

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

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

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 79
a(6) = 310
a(7) = 1251
a(8) = 5151
a(n+9) = n*(2*n+3)*(2*n-1)/(n+10)/(n+8)/(2*n+17)*a(n)+(8*n^3+83*n^2+145*n+55)/(n+10)/(n+8)/(2*n+17)*a(n+1)+1/12*(1151*n^3+8520*n^2+22579*n+18546)/(n+10)/(n+8)/(2*n+17)*a(n+2)-1/24*(2233*n^3+55122*n^2+279635*n+395634)/(n+10)/(n+8)/(2*n+17)*a(n+3)+1/24*(62879*n^3+790140*n^2+3299443*n+4570050)/(n+10)/(n+8)/(2*n+17)*a(n+4)-1/24*(67265*n^3+1013004*n^2+5056489*n+8372154)/(n+10)/(n+8)/(2*n+17)*a(n+5)+1/6*(7612*n^3+136431*n^2+810569*n+1597989)/(n+10)/(n+8)/(2*n+17)*a(n+6)-1/12*(3640*n^3+76029*n^2+526883*n+1212402)/(n+10)/(n+8)/(2*n+17)*a(n+7)+1/12*(458*n^3+10893*n^2+85993*n+225450)/(n+10)/(n+8)/(2*n+17)*a(n+8), n >= 9

Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 79
a \! \left(6\right) = 310
a \! \left(7\right) = 1251
a \! \left(8\right) = 5151
a \! \left(n +9\right) = \frac{n \left(2 n +3\right) \left(2 n -1\right) a \! \left(n \right)}{\left(n +10\right) \left(n +8\right) \left(2 n +17\right)}+\frac{\left(8 n^{3}+83 n^{2}+145 n +55\right) a \! \left(n +1\right)}{\left(n +10\right) \left(n +8\right) \left(2 n +17\right)}+\frac{\left(1151 n^{3}+8520 n^{2}+22579 n +18546\right) a \! \left(n +2\right)}{12 \left(n +10\right) \left(n +8\right) \left(2 n +17\right)}-\frac{\left(2233 n^{3}+55122 n^{2}+279635 n +395634\right) a \! \left(n +3\right)}{24 \left(n +10\right) \left(n +8\right) \left(2 n +17\right)}+\frac{\left(62879 n^{3}+790140 n^{2}+3299443 n +4570050\right) a \! \left(n +4\right)}{24 \left(n +10\right) \left(n +8\right) \left(2 n +17\right)}-\frac{\left(67265 n^{3}+1013004 n^{2}+5056489 n +8372154\right) a \! \left(n +5\right)}{24 \left(n +10\right) \left(n +8\right) \left(2 n +17\right)}+\frac{\left(7612 n^{3}+136431 n^{2}+810569 n +1597989\right) a \! \left(n +6\right)}{6 \left(n +10\right) \left(n +8\right) \left(2 n +17\right)}-\frac{\left(3640 n^{3}+76029 n^{2}+526883 n +1212402\right) a \! \left(n +7\right)}{12 \left(n +10\right) \left(n +8\right) \left(2 n +17\right)}+\frac{\left(458 n^{3}+10893 n^{2}+85993 n +225450\right) a \! \left(n +8\right)}{12 \left(n +10\right) \left(n +8\right) \left(2 n +17\right)}, \quad n \geq 9

Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/234/
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[27,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[27,x]*F[7,x]
F[7,x] = F[42,x]+F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[14,x,k[0]]
F[10,x,k[0]] = F[0,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[9,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[27,x]
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[18,x,k[0]]+F[28,x,k[0]]
F[18,x,k[0]] = F[19,x]*F[21,x,k[0]]
F[19,x] = F[20,x,1]
F[20,x,k[0]] = F[21,x,k[0]]+F[24,x,k[0]]
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[13,x,k[0]]*F[21,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[21,x,k[0]]*F[26,x,k[0]]*F[27,x]
F[26,x,k[0]] = 1/(-1+k[0])*(F[20,x,k[0]]*k[0]-F[20,x,1])
F[27,x] = x
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[19,x]*F[27,x]*F[30,x,k[0]]
F[31,x,k[0]] = F[20,x,k[0]]*F[27,x]*F[30,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]+F[41,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[9,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[39,x,k[0]]
F[35,x,k[0]] = F[21,x,k[0]]*F[36,x,k[0]]
F[20,x,k[0]] = F[36,x,k[0]]+F[37,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[19,x]*F[27,x]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[27,x]*F[30,x,k[0]]*F[36,x,k[0]]
F[41,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]
F[42,x] = F[34,x,1]
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_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{27}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{42}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{27}\! \left(x \right)
F_{16}\! \left(x , y\right) = \frac{y F_{17}\! \left(x , y\right)-F_{17}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{19}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{27}\! \left(x \right)
F_{26}\! \left(x , y\right) = \frac{y F_{20}\! \left(x , y\right)-F_{20}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x \right) = x
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{27}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{27}\! \left(x \right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{42}\! \left(x \right) = F_{34}\! \left(x , 1\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_27(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_27(x)*F_7(x))
Eq(F_7(x), F_42(x) + F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_14(x, k_0))
Eq(F_10(x, k_0), F_0(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_9(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_27(x))
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_18(x, k_0) + F_28(x, k_0))
Eq(F_18(x, k_0), F_19(x)*F_21(x, k_0))
Eq(F_19(x), F_20(x, 1))
Eq(F_20(x, k_0), F_21(x, k_0) + F_24(x, k_0))
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_13(x, k_0)*F_21(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_21(x, k_0)*F_26(x, k_0)*F_27(x))
Eq(F_26(x, k_0), (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_27(x), x)
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_19(x)*F_27(x)*F_30(x, k_0))
Eq(F_31(x, k_0), F_20(x, k_0)*F_27(x)*F_30(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0) + F_41(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_9(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_39(x, k_0))
Eq(F_35(x, k_0), F_21(x, k_0)*F_36(x, k_0))
Eq(F_20(x, k_0), F_36(x, k_0) + F_37(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_19(x)*F_27(x))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_27(x)*F_30(x, k_0)*F_36(x, k_0))
Eq(F_41(x, k_0), F_20(x, k_0)*F_21(x, k_0))
Eq(F_42(x), F_34(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.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_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": 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"pos": [[0, 2], [0, 2], [4, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 4], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [4, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [4, 4], [5, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [4, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [4, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [4, 4], [4, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [4, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[3, 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{"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 3]]}, {"patt": [0, 1], "pos": [[4, 3], [4, 3]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [4, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [4, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [4, 3], [4, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [4, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 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"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"}}, {"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, 0]]}, {"patt": [0], "pos": [[1, 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"pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": 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{"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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]]}]]}, {"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]]}], "requirements": []}], "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]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}

Specification 2
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/235/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[11,x,k[0]]+F[8,x]+F[9,x,k[0]]
F[8,x] = 0
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0]] = F[14,x,k[0]]+F[55,x,k[0]]
F[14,x,k[0]] = F[0,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = F[14,x,k[0]]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[4,x]
F[20,x,k[0]] = 1/(-1+k[0])*(F[21,x,k[0]]*k[0]-F[21,x,1])
F[21,x,k[0]] = F[22,x,k[0]]+F[47,x,k[0]]
F[22,x,k[0]] = F[23,x]*F[44,x,k[0]]
F[23,x] = F[24,x,1]
F[25,x,k[0]] = F[24,x,k[0]]+F[34,x,k[0]]
F[25,x,k[0]] = F[1,x]+F[26,x,k[0]]+F[28,x,k[0]]+F[29,x]
F[26,x,k[0]] = F[27,x,k[0]]*F[4,x]
F[27,x,k[0]] = 1/(-1+k[0])*(F[25,x,k[0]]*k[0]-F[25,x,1])
F[28,x,k[0]] = F[12,x,k[0]]*F[25,x,k[0]]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[1,x]+F[29,x]+F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[23,x]+F[33,x]
F[33,x] = F[34,x,1]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[25,x,k[0]]*F[36,x]*F[4,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x,1]
F[39,x,k[0]] = F[1,x]+F[40,x,k[0]]+F[43,x,k[0]]
F[40,x,k[0]] = F[4,x]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,1,k[0]]
F[42,x,k[0],k[1]] = (F[39,x,k[0]]*k[0]-F[39,x,k[1]]*k[1])/(-k[1]+k[0])
F[43,x,k[0]] = F[12,x,k[0]]*F[39,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[12,x,k[0]]*F[44,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[23,x]*F[4,x]*F[49,x,k[0]]
F[50,x,k[0]] = F[24,x,k[0]]*F[4,x]*F[49,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[52,x,k[0]] = F[51,x,k[0]]+F[54,x,k[0]]
F[53,x,k[0]] = F[12,x,k[0]]*F[52,x,k[0]]
F[53,x,k[0]] = F[7,x,k[0]]
F[54,x,k[0]] = F[24,x,k[0]]*F[44,x,k[0]]
F[55,x,k[0]] = F[7,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \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_{11}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x \right) = 0
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = y x
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{23}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{27}\! \left(x , y\right) = -\frac{-y F_{25}\! \left(x , y\right)+F_{25}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{23}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x , 1\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , 1, y\right)
F_{42}\! \left(x , y , z\right) = \frac{y F_{39}\! \left(x , y\right)-z F_{39}\! \left(x , z\right)}{-z +y}
F_{43}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{44}\! \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 \right) F_{4}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{4}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{7}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_11(x, k_0) + F_8(x) + F_9(x, k_0))
Eq(F_8(x), 0)
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0), F_14(x, k_0) + F_55(x, k_0))
Eq(F_14(x, k_0), F_0(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), F_14(x, k_0) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_4(x))
Eq(F_20(x, k_0), (k_0*F_21(x, k_0) - F_21(x, 1))/(k_0 - 1))
Eq(F_21(x, k_0), F_22(x, k_0) + F_47(x, k_0))
Eq(F_22(x, k_0), F_23(x)*F_44(x, k_0))
Eq(F_23(x), F_24(x, 1))
Eq(F_25(x, k_0), F_24(x, k_0) + F_34(x, k_0))
Eq(F_25(x, k_0), F_1(x) + F_26(x, k_0) + F_28(x, k_0) + F_29(x))
Eq(F_26(x, k_0), F_27(x, k_0)*F_4(x))
Eq(F_27(x, k_0), (k_0*F_25(x, k_0) - F_25(x, 1))/(k_0 - 1))
Eq(F_28(x, k_0), F_12(x, k_0)*F_25(x, k_0))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_1(x) + F_29(x) + F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_23(x) + F_33(x))
Eq(F_33(x), F_34(x, 1))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_25(x, k_0)*F_36(x)*F_4(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x, 1))
Eq(F_39(x, k_0), F_1(x) + F_40(x, k_0) + F_43(x, k_0))
Eq(F_40(x, k_0), F_4(x)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, 1, k_0))
Eq(F_42(x, k_0, k_1), (-k_0*F_39(x, k_0) + k_1*F_39(x, k_1))/(-k_0 + k_1))
Eq(F_43(x, k_0), F_12(x, k_0)*F_39(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_12(x, k_0)*F_44(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_23(x)*F_4(x)*F_49(x, k_0))
Eq(F_50(x, k_0), F_24(x, k_0)*F_4(x)*F_49(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_52(x, k_0), F_51(x, k_0) + F_54(x, k_0))
Eq(F_53(x, k_0), F_12(x, k_0)*F_52(x, k_0))
Eq(F_53(x, k_0), F_7(x, k_0))
Eq(F_54(x, k_0), F_24(x, k_0)*F_44(x, k_0))
Eq(F_55(x, k_0), F_7(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": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.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_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"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, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}], "requirements": []}, {"assumptions": [{"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, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"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, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 2]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 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": 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[{"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 1, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "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]]}], "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]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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]]}]]}, {"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]]}], "requirements": []}], "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]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}

Specification 3
Strategy pack name: pattern_point_placements_tracked_fusion
Tree: http://permpal.com/tree/236/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[41,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[41,x]*F[7,x]
F[7,x] = F[8,x]+F[85,x]
F[8,x] = F[84,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = 1/F[45,x]*F[11,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[83,x,k[0]]
F[15,x,k[0]] = F[14,x,k[0]]+F[70,x,k[0]]
F[15,x,k[0]] = F[16,x]+F[62,x,k[0]]
F[16,x] = -F[17,x]+F[7,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[41,x]
F[19,x] = 1/F[41,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[4,x]+F[22,x]
F[22,x] = 1/F[61,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = -F[25,x]+F[4,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]*F[41,x]
F[27,x] = 1/F[45,x]*F[28,x]
F[28,x] = -F[42,x]+F[29,x]
F[29,x] = F[30,x]+F[8,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[41,x]
F[32,x] = F[33,x,1]
F[33,x,k[0]] = F[34,x,k[0]]+F[38,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[8,x]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[33,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = k[0]*x
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[40,x,k[0]] = F[33,x,k[0]]*F[41,x]
F[41,x] = x
F[42,x] = F[43,x]+F[48,x]
F[43,x] = -F[44,x]+F[8,x]
F[44,x] = F[25,x]*F[45,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[41,x]*F[45,x]
F[48,x] = F[49,x,1]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]*F[59,x]
F[52,x,k[0]] = F[27,x]*F[51,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[49,x,k[0]]+F[54,x,k[0]]
F[14,x,k[0]] = F[54,x,k[0]]+F[55,x,k[0]]
F[55,x,k[0]] = F[25,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[1,x]+F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[37,x,k[0]]*F[56,x,k[0]]
F[59,x] = F[60,x]
F[60,x] = -F[25,x]+F[27,x]
F[61,x] = F[25,x]*F[41,x]
F[62,x,k[0]] = F[63,x,k[0]]+F[64,x,k[0]]
F[63,x,k[0]] = F[12,x,k[0]]
F[65,x,k[0]] = F[64,x,k[0]]+F[80,x]
F[65,x,k[0]] = F[66,x,k[0]]+F[69,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = 1/(-1+k[0])*(F[68,x,k[0]]*k[0]-F[68,x,1])
F[68,x,k[0]] = F[15,x,k[0]]*F[41,x]
F[70,x,k[0]] = F[69,x,k[0]]+F[77,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[41,x]*F[72,x,k[0]]
F[73,x,k[0]] = F[41,x]*F[72,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[49,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[56,x,k[0]]*F[59,x]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[46,x]*F[79,x,k[0]]
F[14,x,k[0]] = F[66,x,k[0]]+F[79,x,k[0]]
F[80,x] = -F[81,x]+F[16,x]
F[81,x] = F[82,x]
F[82,x] = F[0,x]*F[45,x]
F[83,x,k[0]] = F[37,x,k[0]]*F[45,x]
F[84,x] = F[66,x,1]
F[85,x] = F[86,x]
F[86,x] = F[71,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{85}\! \left(x \right)
F_{8}\! \left(x \right) = F_{84}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{45}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{16}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{41}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{61}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{41}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{45}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{41}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = y x
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = -\frac{-y F_{40}\! \left(x , y\right)+F_{40}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = x
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{25}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{41}\! \left(x \right) F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x , 1\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{59}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{61}\! \left(x \right) = F_{25}\! \left(x \right) F_{41}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{80}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = -\frac{-y F_{68}\! \left(x , y\right)+F_{68}\! \left(x , 1\right)}{-1+y}
F_{68}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{70}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{59}\! \left(x \right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{46}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{80}\! \left(x \right) = -F_{81}\! \left(x \right)+F_{16}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{0}\! \left(x \right) F_{45}\! \left(x \right)
F_{83}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{45}\! \left(x \right)
F_{84}\! \left(x \right) = F_{66}\! \left(x , 1\right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{71}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_41(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_41(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_85(x))
Eq(F_8(x), F_84(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x)/F_45(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_83(x, k_0))
Eq(F_15(x, k_0), F_14(x, k_0) + F_70(x, k_0))
Eq(F_15(x, k_0), F_16(x) + F_62(x, k_0))
Eq(F_16(x), -F_17(x) + F_7(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_41(x))
Eq(F_19(x), F_20(x)/F_41(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x) - F_4(x))
Eq(F_22(x), F_23(x)/F_61(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), -F_25(x) + F_4(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x)*F_41(x))
Eq(F_27(x), F_28(x)/F_45(x))
Eq(F_28(x), F_29(x) - F_42(x))
Eq(F_29(x), F_30(x) + F_8(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_41(x))
Eq(F_32(x), F_33(x, 1))
Eq(F_33(x, k_0), F_34(x, k_0) + F_38(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_8(x))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_33(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), k_0*x)
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_33(x, k_0)*F_41(x))
Eq(F_41(x), x)
Eq(F_42(x), F_43(x) + F_48(x))
Eq(F_43(x), -F_44(x) + F_8(x))
Eq(F_44(x), F_25(x)*F_45(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_41(x)*F_45(x))
Eq(F_48(x), F_49(x, 1))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0)*F_59(x))
Eq(F_52(x, k_0), F_27(x)*F_51(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_49(x, k_0) + F_54(x, k_0))
Eq(F_14(x, k_0), F_54(x, k_0) + F_55(x, k_0))
Eq(F_55(x, k_0), F_25(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_1(x) + F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_37(x, k_0)*F_56(x, k_0))
Eq(F_59(x), F_60(x))
Eq(F_60(x), -F_25(x) + F_27(x))
Eq(F_61(x), F_25(x)*F_41(x))
Eq(F_62(x, k_0), F_63(x, k_0) + F_64(x, k_0))
Eq(F_63(x, k_0), F_12(x, k_0))
Eq(F_65(x, k_0), F_64(x, k_0) + F_80(x))
Eq(F_65(x, k_0), F_66(x, k_0) + F_69(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), (k_0*F_68(x, k_0) - F_68(x, 1))/(k_0 - 1))
Eq(F_68(x, k_0), F_15(x, k_0)*F_41(x))
Eq(F_70(x, k_0), F_69(x, k_0) + F_77(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_41(x)*F_72(x, k_0))
Eq(F_73(x, k_0), F_41(x)*F_72(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_49(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_56(x, k_0)*F_59(x))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_46(x)*F_79(x, k_0))
Eq(F_14(x, k_0), F_66(x, k_0) + F_79(x, k_0))
Eq(F_80(x), F_16(x) - F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_0(x)*F_45(x))
Eq(F_83(x, k_0), F_37(x, k_0)*F_45(x))
Eq(F_84(x), F_66(x, 1))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_71(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": true, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}]], "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.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "pattern_point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 4], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [0, 2], [0, 4]], [[1, 3], [2, 0]]], "strategy_class": "FactorStrategy", "workable": false}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], 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"direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": 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[0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", 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Specification 4
Strategy pack name: insertion_point_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/237/
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[0,x]+F[5,x]
F[5,x] = F[48,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[1,x]+F[46,x]+F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]*F[22,x]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[43,x,k[0]]+F[45,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[22,x]
F[13,x,k[0]] = F[14,x,k[0]]+F[26,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x]+F[24,x,k[0]]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[23,x]
F[22,x] = x
F[23,x] = F[1,x]+F[20,x]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[18,x,k[0]]*F[19,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[33,x,k[0]]
F[27,x,k[0]] = F[20,x]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x]+F[30,x,k[0]]+F[32,x,k[0]]
F[29,x] = 0
F[30,x,k[0]] = F[22,x]*F[31,x,k[0]]
F[31,x,k[0]] = F[16,x,k[0]]+F[28,x,k[0]]
F[32,x,k[0]] = F[18,x,k[0]]*F[27,x,k[0]]
F[33,x,k[0]] = F[34,x]+F[39,x,k[0]]
F[34,x] = F[29,x]+F[35,x]+F[37,x]
F[35,x] = F[22,x]*F[36,x]
F[36,x] = F[20,x]+F[34,x]
F[37,x] = F[22,x]*F[38,x]
F[38,x] = F[20,x]+F[34,x]
F[39,x,k[0]] = 2*F[29,x]+F[40,x,k[0]]+F[42,x,k[0]]
F[40,x,k[0]] = F[22,x]*F[41,x,k[0]]
F[41,x,k[0]] = F[24,x,k[0]]+F[39,x,k[0]]
F[42,x,k[0]] = F[18,x,k[0]]*F[33,x,k[0]]
F[43,x,k[0]] = F[22,x]*F[44,x,k[0]]
F[44,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[45,x,k[0]] = F[11,x,k[0]]*F[18,x,k[0]]
F[46,x] = F[22,x]*F[47,x]
F[47,x] = F[23,x]+F[38,x]
F[48,x] = F[49,x]
F[49,x] = F[22,x]*F[50,x]
F[50,x] = F[129,x]+F[51,x]
F[51,x] = F[23,x]*F[52,x]
F[52,x] = F[20,x]+F[53,x]
F[53,x] = F[2,x]+F[54,x]
F[54,x] = F[55,x,1]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[18,x,k[0]]*F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]+F[59,x,k[0]]
F[58,x,k[0]] = F[2,x]+F[55,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[61,x,k[0]]
F[60,x,k[0]] = F[15,x,k[0]]*F[6,x]
F[61,x,k[0]] = F[48,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[22,x]*F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[68,x,k[0]]
F[65,x,k[0]] = F[23,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[24,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = -k[0]*(F[55,x,1]-F[55,x,k[0]])/(-1+k[0])
F[68,x,k[0]] = F[69,x,k[0]]+F[79,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[16,x,k[0]]*F[20,x]*F[71,x]
F[71,x] = F[6,x]+F[72,x]
F[72,x] = F[73,x,1]
F[73,x,k[0]] = F[29,x]+F[74,x,k[0]]+F[77,x,k[0]]
F[74,x,k[0]] = -k[0]*(F[75,x,1]-F[75,x,k[0]])/(-1+k[0])
F[75,x,k[0]] = F[22,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[16,x,k[0]]+F[73,x,k[0]]
F[77,x,k[0]] = F[18,x,k[0]]*F[78,x,k[0]]
F[78,x,k[0]] = F[6,x]+F[73,x,k[0]]
F[79,x,k[0]] = -k[0]*(F[80,x,1]-F[80,x,k[0]])/(-1+k[0])
F[80,x,k[0]] = F[62,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[22,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[87,x,k[0]]
F[84,x,k[0]] = F[72,x]*F[85,x,k[0]]
F[86,x,k[0]] = F[22,x]*F[85,x,k[0]]
F[86,x,k[0]] = F[55,x,k[0]]
F[87,x,k[0]] = F[128,x]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[90,x,k[0]]
F[89,x,k[0]] = F[16,x,k[0]]*F[5,x]
F[90,x,k[0]] = F[91,x,k[0]]+F[99,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[6,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[18,x,k[0]]*F[95,x,k[0]]
F[95,x,k[0]] = F[60,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[97,x,k[0]]*F[98,x]
F[97,x,k[0]] = F[6,x]+F[93,x,k[0]]
F[98,x] = F[1,x]+F[7,x]
F[100,x,k[0]] = F[107,x]+F[99,x,k[0]]
F[101,x,k[0]] = F[100,x,k[0]]+F[105,x,k[0]]
F[102,x,k[0]] = F[101,x,k[0]]+F[104,x,k[0]]
F[103,x,k[0]] = F[102,x,k[0]]*F[18,x,k[0]]
F[103,x,k[0]] = F[62,x,k[0]]
F[104,x,k[0]] = F[15,x,k[0]]*F[48,x]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[6,x]*F[97,x,k[0]]
F[107,x] = -F[126,x]+F[108,x]
F[108,x] = -F[5,x]+F[109,x]
F[109,x] = 1/F[22,x]*F[110,x]
F[110,x] = -F[111,x]-F[29,x]+F[48,x]
F[111,x] = F[112,x]*F[22,x]
F[112,x] = F[113,x]+F[114,x]
F[113,x] = F[2,x]+F[48,x]
F[114,x] = F[115,x]+F[117,x]
F[115,x] = F[116,x]
F[116,x] = F[2,x]*F[20,x]
F[117,x] = F[118,x,1]
F[118,x,k[0]] = 2*F[29,x]+F[119,x,k[0]]+F[121,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]*F[18,x,k[0]]
F[120,x,k[0]] = F[118,x,k[0]]+F[48,x]
F[121,x,k[0]] = -k[0]*(F[122,x,1]-F[122,x,k[0]])/(-1+k[0])
F[122,x,k[0]] = F[123,x,k[0]]*F[22,x]
F[123,x,k[0]] = F[118,x,k[0]]+F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[16,x,k[0]]*F[2,x]
F[126,x] = F[127,x]
F[127,x] = F[6,x]^2
F[128,x] = F[76,x,1]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[20,x]*F[71,x]
F[131,x] = F[132,x]+F[134,x]
F[132,x] = F[133,x]+F[48,x]
F[133,x] = F[62,x,1]
F[134,x] = F[135,x]+F[142,x]
F[135,x] = F[136,x,1]
F[136,x,k[0]] = F[137,x,k[0]]+F[140,x,k[0]]+F[29,x]
F[137,x,k[0]] = -k[0]*(F[138,x,1]-F[138,x,k[0]])/(-1+k[0])
F[138,x,k[0]] = F[139,x,k[0]]*F[22,x]
F[139,x,k[0]] = F[125,x,k[0]]+F[136,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]*F[18,x,k[0]]
F[141,x,k[0]] = F[136,x,k[0]]+F[48,x]
F[142,x] = F[81,x,1]
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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{48}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \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) = F_{11}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)+F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{35}\! \left(x \right) = F_{22}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{39}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{45}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{22}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{129}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{23}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{20}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{61}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{23}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = -\frac{y \left(F_{55}\! \left(x , 1\right)-F_{55}\! \left(x , y\right)\right)}{-1+y}
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{6}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x , 1\right)
F_{73}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{74}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = -\frac{y \left(F_{75}\! \left(x , 1\right)-F_{75}\! \left(x , y\right)\right)}{-1+y}
F_{75}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{6}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = -\frac{y \left(F_{80}\! \left(x , 1\right)-F_{80}\! \left(x , y\right)\right)}{-1+y}
F_{80}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{72}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{128}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{97}\! \left(x , y\right) F_{98}\! \left(x \right)
F_{97}\! \left(x , y\right) = F_{6}\! \left(x \right)+F_{93}\! \left(x , y\right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{107}\! \left(x \right)+F_{99}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{48}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{107}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = \frac{F_{110}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{110}\! \left(x \right) = -F_{111}\! \left(x \right)-F_{29}\! \left(x \right)+F_{48}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{22}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{113}\! \left(x \right) = F_{2}\! \left(x \right)+F_{48}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{2}\! \left(x \right) F_{20}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x , 1\right)
F_{118}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{119}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{121}\! \left(x , y\right) = -\frac{y \left(F_{122}\! \left(x , 1\right)-F_{122}\! \left(x , y\right)\right)}{-1+y}
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{6} \left(x \right)^{2}
F_{128}\! \left(x \right) = F_{76}\! \left(x , 1\right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{134}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{48}\! \left(x \right)
F_{133}\! \left(x \right) = F_{62}\! \left(x , 1\right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{142}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x , 1\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{140}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{137}\! \left(x , y\right) = -\frac{y \left(F_{138}\! \left(x , 1\right)-F_{138}\! \left(x , y\right)\right)}{-1+y}
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{142}\! \left(x \right) = F_{81}\! \left(x , 1\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_0(x) + F_5(x))
Eq(F_5(x), F_48(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_1(x) + F_46(x) + F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_22(x))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_43(x, k_0) + F_45(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_22(x))
Eq(F_13(x, k_0), F_14(x, k_0) + F_26(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x) + F_24(x, k_0))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_23(x))
Eq(F_22(x), x)
Eq(F_23(x), F_1(x) + F_20(x))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_18(x, k_0)*F_19(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_33(x, k_0))
Eq(F_27(x, k_0), F_20(x) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x) + F_30(x, k_0) + F_32(x, k_0))
Eq(F_29(x), 0)
Eq(F_30(x, k_0), F_22(x)*F_31(x, k_0))
Eq(F_31(x, k_0), F_16(x, k_0) + F_28(x, k_0))
Eq(F_32(x, k_0), F_18(x, k_0)*F_27(x, k_0))
Eq(F_33(x, k_0), F_34(x) + F_39(x, k_0))
Eq(F_34(x), F_29(x) + F_35(x) + F_37(x))
Eq(F_35(x), F_22(x)*F_36(x))
Eq(F_36(x), F_20(x) + F_34(x))
Eq(F_37(x), F_22(x)*F_38(x))
Eq(F_38(x), F_20(x) + F_34(x))
Eq(F_39(x, k_0), 2*F_29(x) + F_40(x, k_0) + F_42(x, k_0))
Eq(F_40(x, k_0), F_22(x)*F_41(x, k_0))
Eq(F_41(x, k_0), F_24(x, k_0) + F_39(x, k_0))
Eq(F_42(x, k_0), F_18(x, k_0)*F_33(x, k_0))
Eq(F_43(x, k_0), F_22(x)*F_44(x, k_0))
Eq(F_44(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_45(x, k_0), F_11(x, k_0)*F_18(x, k_0))
Eq(F_46(x), F_22(x)*F_47(x))
Eq(F_47(x), F_23(x) + F_38(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_22(x)*F_50(x))
Eq(F_50(x), F_129(x) + F_51(x))
Eq(F_51(x), F_23(x)*F_52(x))
Eq(F_52(x), F_20(x) + F_53(x))
Eq(F_53(x), F_2(x) + F_54(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_18(x, k_0)*F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0) + F_59(x, k_0))
Eq(F_58(x, k_0), F_2(x) + F_55(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_61(x, k_0))
Eq(F_60(x, k_0), F_15(x, k_0)*F_6(x))
Eq(F_61(x, k_0), F_48(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_22(x)*F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_68(x, k_0))
Eq(F_65(x, k_0), F_23(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_24(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), -F_55(x, 1) + (k_0*F_55(x, k_0) - F_55(x, 1))/(k_0 - 1))
Eq(F_68(x, k_0), F_69(x, k_0) + F_79(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_16(x, k_0)*F_20(x)*F_71(x))
Eq(F_71(x), F_6(x) + F_72(x))
Eq(F_72(x), F_73(x, 1))
Eq(F_73(x, k_0), F_29(x) + F_74(x, k_0) + F_77(x, k_0))
Eq(F_74(x, k_0), -F_75(x, 1) + (k_0*F_75(x, k_0) - F_75(x, 1))/(k_0 - 1))
Eq(F_75(x, k_0), F_22(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_16(x, k_0) + F_73(x, k_0))
Eq(F_77(x, k_0), F_18(x, k_0)*F_78(x, k_0))
Eq(F_78(x, k_0), F_6(x) + F_73(x, k_0))
Eq(F_79(x, k_0), -F_80(x, 1) + (k_0*F_80(x, k_0) - F_80(x, 1))/(k_0 - 1))
Eq(F_80(x, k_0), F_62(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_22(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_87(x, k_0))
Eq(F_84(x, k_0), F_72(x)*F_85(x, k_0))
Eq(F_86(x, k_0), F_22(x)*F_85(x, k_0))
Eq(F_86(x, k_0), F_55(x, k_0))
Eq(F_87(x, k_0), F_128(x)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_90(x, k_0))
Eq(F_89(x, k_0), F_16(x, k_0)*F_5(x))
Eq(F_90(x, k_0), F_91(x, k_0) + F_99(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_6(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_18(x, k_0)*F_95(x, k_0))
Eq(F_95(x, k_0), F_60(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_97(x, k_0)*F_98(x))
Eq(F_97(x, k_0), F_6(x) + F_93(x, k_0))
Eq(F_98(x), F_1(x) + F_7(x))
Eq(F_100(x, k_0), F_107(x) + F_99(x, k_0))
Eq(F_101(x, k_0), F_100(x, k_0) + F_105(x, k_0))
Eq(F_102(x, k_0), F_101(x, k_0) + F_104(x, k_0))
Eq(F_103(x, k_0), F_102(x, k_0)*F_18(x, k_0))
Eq(F_103(x, k_0), F_62(x, k_0))
Eq(F_104(x, k_0), F_15(x, k_0)*F_48(x))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_6(x)*F_97(x, k_0))
Eq(F_107(x), F_108(x) - F_126(x))
Eq(F_108(x), F_109(x) - F_5(x))
Eq(F_109(x), F_110(x)/F_22(x))
Eq(F_110(x), -F_111(x) - F_29(x) + F_48(x))
Eq(F_111(x), F_112(x)*F_22(x))
Eq(F_112(x), F_113(x) + F_114(x))
Eq(F_113(x), F_2(x) + F_48(x))
Eq(F_114(x), F_115(x) + F_117(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_2(x)*F_20(x))
Eq(F_117(x), F_118(x, 1))
Eq(F_118(x, k_0), F_119(x, k_0) + F_121(x, k_0) + 2*F_29(x))
Eq(F_119(x, k_0), F_120(x, k_0)*F_18(x, k_0))
Eq(F_120(x, k_0), F_118(x, k_0) + F_48(x))
Eq(F_121(x, k_0), -F_122(x, 1) + (-k_0*F_122(x, k_0) + F_122(x, 1))/(1 - k_0))
Eq(F_122(x, k_0), F_123(x, k_0)*F_22(x))
Eq(F_123(x, k_0), F_118(x, k_0) + F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_16(x, k_0)*F_2(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_6(x)**2)
Eq(F_128(x), F_76(x, 1))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_20(x)*F_71(x))
Eq(F_131(x), F_132(x) + F_134(x))
Eq(F_132(x), F_133(x) + F_48(x))
Eq(F_133(x), F_62(x, 1))
Eq(F_134(x), F_135(x) + F_142(x))
Eq(F_135(x), F_136(x, 1))
Eq(F_136(x, k_0), F_137(x, k_0) + F_140(x, k_0) + F_29(x))
Eq(F_137(x, k_0), -F_138(x, 1) + (k_0*F_138(x, k_0) - F_138(x, 1))/(k_0 - 1))
Eq(F_138(x, k_0), F_139(x, k_0)*F_22(x))
Eq(F_139(x, k_0), F_125(x, k_0) + F_136(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0)*F_18(x, k_0))
Eq(F_141(x, k_0), F_136(x, k_0) + F_48(x))
Eq(F_142(x), F_81(x, 1))
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"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"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], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [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, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "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"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [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, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": 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"strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}]}

Specification 5
Strategy pack name: all_the_strategies_2_tracked_fusion
Tree: http://permpal.com/tree/238/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[9,x,1]
F[10,x,k[0]] = F[18,x,k[0]]*F[9,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x]+F[13,x,k[0]]+F[15,x,k[0]]
F[12,x] = 0
F[13,x,k[0]] = F[14,x,k[0]]*F[7,x]
F[14,x,k[0]] = -k[0]*(F[11,x,1]-F[11,x,k[0]])/(-1+k[0])
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[12,x]+F[17,x,k[0]]+F[82,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[19,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[0,x]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[18,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = F[19,x,k[0]]+F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[7,x]
F[25,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[26,x,k[0]] = F[27,x,k[0]]+F[55,x,k[0]]
F[27,x,k[0]] = F[28,x]*F[52,x,k[0]]
F[28,x] = 1/F[7,x]*F[29,x]
F[29,x] = -F[12,x]-F[50,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[7,x]
F[32,x] = F[33,x,1]
F[33,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[36,x,k[0]]+F[37,x]
F[34,x,k[0]] = F[35,x,k[0]]*F[7,x]
F[35,x,k[0]] = 1/(-1+k[0])*(F[33,x,k[0]]*k[0]-F[33,x,1])
F[36,x,k[0]] = F[18,x,k[0]]*F[33,x,k[0]]
F[37,x] = F[38,x]*F[7,x]
F[38,x] = -F[41,x]+F[39,x]
F[39,x] = 1/F[7,x]*F[40,x]
F[40,x] = F[2,x]
F[41,x] = -F[47,x]+F[42,x]
F[42,x] = 1/F[7,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[7,x]
F[46,x] = F[44,x]+F[5,x]
F[47,x] = F[12,x]+F[48,x]+F[49,x]
F[48,x] = F[32,x]*F[7,x]
F[49,x] = F[47,x]*F[7,x]
F[50,x] = F[51,x]
F[51,x] = F[7,x]^2*F[28,x]*F[38,x]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[18,x,k[0]]*F[52,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[28,x]*F[57,x,k[0]]*F[7,x]
F[58,x,k[0]] = F[57,x,k[0]]*F[7,x]
F[58,x,k[0]] = F[59,x,k[0]]
F[22,x,k[0]] = F[52,x,k[0]]+F[59,x,k[0]]+F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]*F[7,x]
F[62,x,k[0]] = F[18,x,k[0]]*F[61,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[18,x,k[0]]*F[64,x,k[0]]
F[65,x,k[0]] = F[52,x,k[0]]*F[64,x,k[0]]*F[7,x]
F[65,x,k[0]] = F[66,x,k[0]]
F[67,x,k[0]] = F[52,x,k[0]]+F[66,x,k[0]]+F[79,x,k[0]]
F[67,x,k[0]] = F[4,x]+F[68,x,k[0]]
F[69,x,k[0]] = F[68,x,k[0]]+F[75,x,k[0]]
F[70,x,k[0]] = F[18,x,k[0]]*F[69,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[72,x,k[0]] = F[71,x,k[0]]+F[73,x,k[0]]
F[72,x,k[0]] = F[11,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[18,x,k[0]]*F[4,x]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[18,x,k[0]]*F[77,x,k[0]]
F[78,x,k[0]] = F[18,x,k[0]]*F[77,x,k[0]]
F[9,x,k[0]] = F[22,x,k[0]]+F[78,x,k[0]]
F[79,x,k[0]] = F[7,x]*F[80,x,k[0]]
F[81,x,k[0]] = F[18,x,k[0]]*F[80,x,k[0]]
F[67,x,k[0]] = F[4,x]+F[81,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[18,x,k[0]]^2*F[9,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_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{12}\! \left(x \right) = 0
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{14}\! \left(x , y\right) = -\frac{y \left(F_{11}\! \left(x , 1\right)-F_{11}\! \left(x , y\right)\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{7}\! \left(x \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_{27}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{29}\! \left(x \right) = -F_{12}\! \left(x \right)-F_{50}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{7}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{33}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{37}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{35}\! \left(x , y\right) = -\frac{-y F_{33}\! \left(x , y\right)+F_{33}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)+F_{5}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)+F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{32}\! \left(x \right) F_{7}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47}\! \left(x \right) F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{7} \left(x \right)^{2} F_{28}\! \left(x \right) F_{38}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{57}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{59}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{64}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{64}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{66}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{68}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{18}\! \left(x , y\right)^{2} F_{9}\! \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_4(x)*F_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_9(x, 1))
Eq(F_10(x, k_0), F_18(x, k_0)*F_9(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x) + F_13(x, k_0) + F_15(x, k_0))
Eq(F_12(x), 0)
Eq(F_13(x, k_0), F_14(x, k_0)*F_7(x))
Eq(F_14(x, k_0), -F_11(x, 1) + (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_12(x) + F_17(x, k_0) + F_82(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_19(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_0(x) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_18(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), F_19(x, k_0) + F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_7(x))
Eq(F_25(x, k_0), (k_0*F_26(x, k_0) - F_26(x, 1))/(k_0 - 1))
Eq(F_26(x, k_0), F_27(x, k_0) + F_55(x, k_0))
Eq(F_27(x, k_0), F_28(x)*F_52(x, k_0))
Eq(F_28(x), F_29(x)/F_7(x))
Eq(F_29(x), -F_12(x) + F_30(x) - F_50(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_7(x))
Eq(F_32(x), F_33(x, 1))
Eq(F_33(x, k_0), F_1(x) + F_34(x, k_0) + F_36(x, k_0) + F_37(x))
Eq(F_34(x, k_0), F_35(x, k_0)*F_7(x))
Eq(F_35(x, k_0), (k_0*F_33(x, k_0) - F_33(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_18(x, k_0)*F_33(x, k_0))
Eq(F_37(x), F_38(x)*F_7(x))
Eq(F_38(x), F_39(x) - F_41(x))
Eq(F_39(x), F_40(x)/F_7(x))
Eq(F_40(x), F_2(x))
Eq(F_41(x), F_42(x) - F_47(x))
Eq(F_42(x), F_43(x)/F_7(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_7(x))
Eq(F_46(x), F_44(x) + F_5(x))
Eq(F_47(x), F_12(x) + F_48(x) + F_49(x))
Eq(F_48(x), F_32(x)*F_7(x))
Eq(F_49(x), F_47(x)*F_7(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_28(x)*F_38(x)*F_7(x)**2)
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_18(x, k_0)*F_52(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_28(x)*F_57(x, k_0)*F_7(x))
Eq(F_58(x, k_0), F_57(x, k_0)*F_7(x))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_22(x, k_0), F_52(x, k_0) + F_59(x, k_0) + F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0)*F_7(x))
Eq(F_62(x, k_0), F_18(x, k_0)*F_61(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_18(x, k_0)*F_64(x, k_0))
Eq(F_65(x, k_0), F_52(x, k_0)*F_64(x, k_0)*F_7(x))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_67(x, k_0), F_52(x, k_0) + F_66(x, k_0) + F_79(x, k_0))
Eq(F_67(x, k_0), F_4(x) + F_68(x, k_0))
Eq(F_69(x, k_0), F_68(x, k_0) + F_75(x, k_0))
Eq(F_70(x, k_0), F_18(x, k_0)*F_69(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_72(x, k_0), F_71(x, k_0) + F_73(x, k_0))
Eq(F_72(x, k_0), F_11(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_18(x, k_0)*F_4(x))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_18(x, k_0)*F_77(x, k_0))
Eq(F_78(x, k_0), F_18(x, k_0)*F_77(x, k_0))
Eq(F_9(x, k_0), F_22(x, k_0) + F_78(x, k_0))
Eq(F_79(x, k_0), F_7(x)*F_80(x, k_0))
Eq(F_81(x, k_0), F_18(x, k_0)*F_80(x, k_0))
Eq(F_67(x, k_0), F_4(x) + F_81(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_18(x, k_0)**2*F_9(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 2, "strategy_class": "RequirementInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "ignore_parent": false, "strategy_class": "AllPlacementsFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "all_the_strategies_2_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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