0123_0231_3012

Counting sequence:
1, 1, 2, 6, 21, 76, 275, 991, 3566, 12850, 46458, 168686, 615340, 2255101, 8301270, 30684958, 113860149, 423982381, 1583896545, 5934619813, 22296759999, 83980806061, 317047544619, 1199500330579, 4547171538809, 17269807475089, 65702973241073, 250371745697785, 955530058679253, 3651927331186778, 13975977110449303, 53553911408118871, 205455911321597118, 789108041999561198, 3034022894989657866, 11677287114528415982, 44986658863408260528, 173469756063383393986, 669488428943465408228, 2585973194540250343596, 9996550371002335195182, 38672847622289419991494, 149719254709081700420118, 580031054724116766385966, 2248611014995369233374802, 8722783688350747583316124, 33858089274580929343725558, 131500047166244910557582758, 511017343690031288328783420, 1986928992133832675955264844, 7729604111845029039793260852, 30085141229609819710656803740, 117154480533288052451037132768, 456425977811278910559659290876, 1779013952468334018376505542584, 6937119948805499981271189872200, 27062227526986057846564722725556, 105615173279615682122232344976676, 412345985980504600653444757010724, 1610513701738008867336126223677364, 6292584383245586536684056284367084, 24595217001679916695437724636571161, 96166652152247123736078763839907998, 376136967165122450734029139234565710, 1471671493301054173222075542306231381, 5759899668035915324930569616072961973, 22550395514243356589210559099841333857, 88313033451629104980059334883883477125, 345957846246644231031705035971419709911, 1355644476876185385129073817075026962433, 5313605603186667687917409547331647063227, 20832936091625043877772053548438842264515, 81700780921078358033261733248836151622381, 320489287547431387312858719775348017669253, 1257504504152435675069384570900957445089397, 4935277179655521224846846976555710687035885, 19373891636753851663602110470968864675089601, 76071669777745623687103149902875796744021023, 298763362560587412299128369896279501101189357, 1173620441379748355359254479323607723013067165, 4611281587107818254868097756202561136165086031, 18122039307868683832990874487418185880576163743, 71233094658332081552683268928230747497817617527, 280055316399021554541404187397827355093908153455, 1101263160260997469296387439857416651326858245691, 4331334897403805927490409462839514556040107814463, 17038600789524962680839759453594981759077596102947, 67038734621365027525319046317669860635738170443475, 263812684083822861407716680595631827500544729969191, 1038345398340771266258711459706061737094070968278263, 4087546384403473112161103932138457572532821574740407, 16093727873555414965536662905603541146847627563776295, 63375616594113442577912675378928677734688889598305071, 249607625796404282376255187995906742409470998469809873, 983245974853812422774034894394020098165640238261009827, 3873769656218810579285659658020385852727023086488843235, 15264105186487641637342117732640192236781256862685533401, 60155250868528942727666566197619205380162232058733508473, 237104120475935827052189905538419157893553991141583853457, 934688278054944966272591287819356190595115676733882359225, 3685152216991121386326239073994899960041558396726009356461

Generating function in Maple syntax:
((-6*x^4+19*x^3-18*x^2+7*x-1)*(1-4*x)^(1/2)-2*x^5+22*x^4-43*x^3+30*x^2-9*x+1)/(4*x^5-6*x^4+2*x^3)

Generating function in latex syntax:
\frac{\left(-6 x^{4}+19 x^{3}-18 x^{2}+7 x -1\right) \sqrt{1-4 x}-2 x^{5}+22 x^{4}-43 x^{3}+30 x^{2}-9 x +1}{4 x^{5}-6 x^{4}+2 x^{3}}

Generating function in sympy syntax:
(-2*x**5 + 22*x**4 - 43*x**3 + 30*x**2 - 9*x + sqrt(1 - 4*x)*(-6*x**4 + 19*x**3 - 18*x**2 + 7*x - 1) + 1)/(4*x**5 - 6*x**4 + 2*x**3)

Implicit equation for the generating function in Maple syntax:
x^3*(2*x-1)^2*(x-1)^2*F(x)^2+(2*x-1)*(x-1)*(2*x^5-22*x^4+43*x^3-30*x^2+9*x-1)*F(x)+x^7+14*x^6-73*x^5+131*x^4-111*x^3+49*x^2-11*x+1 = 0

Implicit equation for the generating function in latex syntax:
x^{3} \left(2 x -1\right)^{2} \left(x -1\right)^{2} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(x -1\right) \left(2 x^{5}-22 x^{4}+43 x^{3}-30 x^{2}+9 x -1\right) F \! \left(x \right)+x^{7}+14 x^{6}-73 x^{5}+131 x^{4}-111 x^{3}+49 x^{2}-11 x +1 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 76
a(6) = 275
a(7) = 991
a(n+7) = 24*(2*n+1)/(10+n)*a(n)-(447*n+1982)/(10+n)*a(3+n)-4*(59*n+110)/(10+n)*a(n+1)+2*(226*n+709)/(10+n)*a(n+2)+(1450+251*n)/(10+n)*a(n+4)-(81*n+580)/(10+n)*a(n+5)+2*(7*n+60)/(10+n)*a(n+6), n >= 8

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) = 76
a \! \left(6\right) = 275
a \! \left(7\right) = 991
a \! \left(n +7\right) = \frac{24 \left(2 n +1\right) a \! \left(n \right)}{10+n}-\frac{\left(447 n +1982\right) a \! \left(3+n \right)}{10+n}-\frac{4 \left(59 n +110\right) a \! \left(n +1\right)}{10+n}+\frac{2 \left(226 n +709\right) a \! \left(n +2\right)}{10+n}+\frac{\left(1450+251 n \right) a \! \left(n +4\right)}{10+n}-\frac{\left(81 n +580\right) a \! \left(n +5\right)}{10+n}+\frac{2 \left(7 n +60\right) a \! \left(n +6\right)}{10+n}, \quad n \geq 8

Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_isolated_single_fusion
Tree: http://permpal.com/tree/241/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[48,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[7,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = F[14,x]+F[46,x,k[0]]
F[14,x] = F[15,x]+F[20,x]
F[15,x] = F[16,x,1]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[19,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[3,x]
F[18,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[19,x,k[0]] = F[16,x,k[0]]*F[9,x,k[0]]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[3,x]
F[22,x] = F[15,x]+F[21,x]+F[23,x]+F[44,x]
F[23,x] = F[24,x]
F[24,x] = F[15,x]*F[25,x]*F[3,x]
F[25,x] = F[26,x]+F[36,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[27,x]*F[3,x]
F[30,x] = F[28,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]+F[35,x]
F[32,x] = 0
F[33,x] = F[3,x]*F[34,x]
F[34,x] = F[28,x]+F[31,x]
F[35,x] = F[3,x]*F[30,x]
F[36,x] = F[37,x]
F[37,x] = F[26,x]*F[3,x]*F[38,x]
F[38,x] = F[27,x]+F[39,x]
F[39,x] = F[28,x]+F[40,x]
F[40,x] = F[32,x]+F[41,x]+F[43,x]
F[41,x] = F[3,x]*F[42,x]
F[42,x] = F[28,x]+F[40,x]
F[43,x] = F[3,x]*F[39,x]
F[44,x] = F[45,x]
F[45,x] = F[25,x]*F[27,x]*F[3,x]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[13,x,k[0]]*F[27,x]*F[9,x,k[0]]
F[48,x] = F[14,x]*F[3,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \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_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{7}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = \frac{y F_{7}\! \left(x , y\right)-F_{7}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y\right) = \frac{y F_{16}\! \left(x , y\right)-F_{16}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{9}\! \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_{3}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)+F_{44}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right) F_{3}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{36}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{3}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{3}\! \left(x \right) F_{30}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{26}\! \left(x \right) F_{3}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{28}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{41}\! \left(x \right) = F_{3}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{28}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{3}\! \left(x \right) F_{39}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{25}\! \left(x \right) F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{27}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{48}\! \left(x \right) = F_{14}\! \left(x \right) F_{3}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_48(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_7(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), F_14(x) + F_46(x, k_0))
Eq(F_14(x), F_15(x) + F_20(x))
Eq(F_15(x), F_16(x, 1))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0) + F_19(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_3(x))
Eq(F_18(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), F_16(x, k_0)*F_9(x, k_0))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_3(x))
Eq(F_22(x), F_15(x) + F_21(x) + F_23(x) + F_44(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_15(x)*F_25(x)*F_3(x))
Eq(F_25(x), F_26(x) + F_36(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_27(x)*F_3(x))
Eq(F_30(x), F_28(x) + F_31(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_35(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_3(x)*F_34(x))
Eq(F_34(x), F_28(x) + F_31(x))
Eq(F_35(x), F_3(x)*F_30(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_26(x)*F_3(x)*F_38(x))
Eq(F_38(x), F_27(x) + F_39(x))
Eq(F_39(x), F_28(x) + F_40(x))
Eq(F_40(x), F_32(x) + F_41(x) + F_43(x))
Eq(F_41(x), F_3(x)*F_42(x))
Eq(F_42(x), F_28(x) + F_40(x))
Eq(F_43(x), F_3(x)*F_39(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_25(x)*F_27(x)*F_3(x))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_13(x, k_0)*F_27(x)*F_9(x, k_0))
Eq(F_48(x), F_14(x)*F_3(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_and_col_placements_tracked_fusion_isolated_single_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}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, 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[0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 2]], [[1, 0], [1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 2
Strategy pack name: col_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/242/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[111,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[7,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[14,x,k[0]]+F[15,x]+F[97,x]
F[14,x,k[0]] = F[13,x,k[0]]*F[9,x,k[0]]
F[15,x] = F[16,x]*F[3,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[51,x,k[0]]+F[53,x,k[0]]+F[88,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[9,x,k[0]]
F[19,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[20,x,k[0]]+F[22,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[3,x]
F[21,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[22,x,k[0]] = F[23,x,k[0]]*F[3,x]
F[23,x,k[0]] = F[24,x]+F[34,x,k[0]]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]*F[3,x]
F[28,x] = F[26,x]+F[29,x]
F[29,x] = F[30,x]+F[31,x]+F[33,x]
F[30,x] = 0
F[31,x] = F[3,x]*F[32,x]
F[32,x] = F[26,x]+F[29,x]
F[33,x] = F[28,x]*F[3,x]
F[34,x,k[0]] = F[35,x,k[0]]+F[43,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[39,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[9,x,k[0]]
F[38,x,k[0]] = F[1,x]+F[36,x,k[0]]
F[39,x,k[0]] = F[30,x]+F[40,x,k[0]]+F[42,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[9,x,k[0]]
F[41,x,k[0]] = F[26,x]+F[39,x,k[0]]
F[42,x,k[0]] = F[3,x]*F[35,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[3,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[36,x,k[0]]+F[44,x,k[0]]
F[47,x,k[0]] = 2*F[30,x]+F[48,x,k[0]]+F[50,x,k[0]]
F[48,x,k[0]] = F[3,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[39,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = F[3,x]*F[43,x,k[0]]
F[51,x,k[0]] = F[3,x]*F[52,x,k[0]]
F[52,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[53,x,k[0]] = F[3,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x]+F[69,x,k[0]]
F[55,x] = F[56,x]+F[60,x]
F[56,x] = F[25,x]+F[57,x]
F[57,x] = F[26,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[3,x]*F[57,x]
F[60,x] = F[61,x]+F[65,x]
F[61,x] = F[26,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[3,x]*F[64,x]
F[64,x] = F[26,x]+F[62,x]
F[65,x] = F[29,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[3,x]*F[68,x]
F[68,x] = F[58,x]+F[66,x]
F[69,x,k[0]] = F[70,x,k[0]]+F[79,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]+F[75,x,k[0]]
F[71,x,k[0]] = F[36,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]*F[9,x,k[0]]
F[74,x,k[0]] = F[26,x]+F[72,x,k[0]]
F[75,x,k[0]] = F[39,x,k[0]]+F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]*F[9,x,k[0]]
F[78,x,k[0]] = F[58,x]+F[76,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[84,x,k[0]]
F[80,x,k[0]] = F[44,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[3,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[72,x,k[0]]+F[81,x,k[0]]
F[84,x,k[0]] = F[47,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[3,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[76,x,k[0]]+F[85,x,k[0]]
F[88,x,k[0]] = F[3,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[1,x]+F[15,x]+F[88,x,k[0]]+F[90,x,k[0]]+F[97,x]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[38,x,k[0]]*F[9,x,k[0]]*F[92,x]
F[92,x] = F[93,x,1]
F[93,x,k[0]] = F[1,x]+F[94,x,k[0]]+F[96,x,k[0]]
F[94,x,k[0]] = F[3,x]*F[95,x,k[0]]
F[95,x,k[0]] = 1/(-1+k[0])*(F[93,x,k[0]]*k[0]-F[93,x,1])
F[96,x,k[0]] = F[9,x,k[0]]*F[93,x,k[0]]
F[97,x] = F[98,x,1]
F[98,x,k[0]] = F[9,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[101,x,k[0]]
F[100,x,k[0]] = F[25,x]+F[46,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[61,x]
F[102,x,k[0]] = F[103,x,k[0]]+F[108,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[106,x,k[0]]+F[30,x]
F[104,x,k[0]] = F[105,x,k[0]]*F[3,x]
F[105,x,k[0]] = F[103,x,k[0]]+F[36,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[9,x,k[0]]
F[107,x,k[0]] = F[103,x,k[0]]+F[26,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[3,x]
F[110,x,k[0]] = F[108,x,k[0]]+F[44,x,k[0]]
F[111,x] = F[112,x]*F[3,x]
F[112,x] = F[1,x]+F[111,x]+F[15,x]+F[97,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{111}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \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_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{7}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{15}\! \left(x \right)+F_{97}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \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_{27}\! \left(x \right) = F_{25}\! \left(x \right) F_{3}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x \right) = F_{3}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{28}\! \left(x \right) F_{3}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{53}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{25}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{26}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{3}\! \left(x \right) F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{26}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{3}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{26}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{29}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{3}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{58}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{76}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{44}\! \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_{3}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{88}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{9}\! \left(x , y\right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x , 1\right)
F_{93}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{94}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = -\frac{-y F_{93}\! \left(x , y\right)+F_{93}\! \left(x , 1\right)}{-1+y}
F_{96}\! \left(x , y\right) = F_{9}\! \left(x , y\right) F_{93}\! \left(x , y\right)
F_{97}\! \left(x \right) = F_{98}\! \left(x , 1\right)
F_{98}\! \left(x , y\right) = F_{9}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{101}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{61}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{3}\! \left(x \right)
F_{112}\! \left(x \right) = F_{1}\! \left(x \right)+F_{111}\! \left(x \right)+F_{15}\! \left(x \right)+F_{97}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_111(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_7(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), F_1(x) + F_12(x, k_0) + F_14(x, k_0) + F_15(x) + F_97(x))
Eq(F_14(x, k_0), F_13(x, k_0)*F_9(x, k_0))
Eq(F_15(x), F_16(x)*F_3(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_51(x, k_0) + F_53(x, k_0) + F_88(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_9(x, k_0))
Eq(F_19(x, k_0), F_1(x) + F_18(x, k_0) + F_20(x, k_0) + F_22(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_3(x))
Eq(F_21(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_3(x))
Eq(F_23(x, k_0), F_24(x) + F_34(x, k_0))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_25(x)*F_3(x))
Eq(F_28(x), F_26(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_31(x) + F_33(x))
Eq(F_30(x), 0)
Eq(F_31(x), F_3(x)*F_32(x))
Eq(F_32(x), F_26(x) + F_29(x))
Eq(F_33(x), F_28(x)*F_3(x))
Eq(F_34(x, k_0), F_35(x, k_0) + F_43(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_39(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_9(x, k_0))
Eq(F_38(x, k_0), F_1(x) + F_36(x, k_0))
Eq(F_39(x, k_0), F_30(x) + F_40(x, k_0) + F_42(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_9(x, k_0))
Eq(F_41(x, k_0), F_26(x) + F_39(x, k_0))
Eq(F_42(x, k_0), F_3(x)*F_35(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_3(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_36(x, k_0) + F_44(x, k_0))
Eq(F_47(x, k_0), 2*F_30(x) + F_48(x, k_0) + F_50(x, k_0))
Eq(F_48(x, k_0), F_3(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_39(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), F_3(x)*F_43(x, k_0))
Eq(F_51(x, k_0), F_3(x)*F_52(x, k_0))
Eq(F_52(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_53(x, k_0), F_3(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x) + F_69(x, k_0))
Eq(F_55(x), F_56(x) + F_60(x))
Eq(F_56(x), F_25(x) + F_57(x))
Eq(F_57(x), F_26(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_3(x)*F_57(x))
Eq(F_60(x), F_61(x) + F_65(x))
Eq(F_61(x), F_26(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_3(x)*F_64(x))
Eq(F_64(x), F_26(x) + F_62(x))
Eq(F_65(x), F_29(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_3(x)*F_68(x))
Eq(F_68(x), F_58(x) + F_66(x))
Eq(F_69(x, k_0), F_70(x, k_0) + F_79(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0) + F_75(x, k_0))
Eq(F_71(x, k_0), F_36(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0)*F_9(x, k_0))
Eq(F_74(x, k_0), F_26(x) + F_72(x, k_0))
Eq(F_75(x, k_0), F_39(x, k_0) + F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0)*F_9(x, k_0))
Eq(F_78(x, k_0), F_58(x) + F_76(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_84(x, k_0))
Eq(F_80(x, k_0), F_44(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_3(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_72(x, k_0) + F_81(x, k_0))
Eq(F_84(x, k_0), F_47(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_3(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_76(x, k_0) + F_85(x, k_0))
Eq(F_88(x, k_0), F_3(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_1(x) + F_15(x) + F_88(x, k_0) + F_90(x, k_0) + F_97(x))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_38(x, k_0)*F_9(x, k_0)*F_92(x))
Eq(F_92(x), F_93(x, 1))
Eq(F_93(x, k_0), F_1(x) + F_94(x, k_0) + F_96(x, k_0))
Eq(F_94(x, k_0), F_3(x)*F_95(x, k_0))
Eq(F_95(x, k_0), (k_0*F_93(x, k_0) - F_93(x, 1))/(k_0 - 1))
Eq(F_96(x, k_0), F_9(x, k_0)*F_93(x, k_0))
Eq(F_97(x), F_98(x, 1))
Eq(F_98(x, k_0), F_9(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_101(x, k_0))
Eq(F_100(x, k_0), F_25(x) + F_46(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_61(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_108(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_106(x, k_0) + F_30(x))
Eq(F_104(x, k_0), F_105(x, k_0)*F_3(x))
Eq(F_105(x, k_0), F_103(x, k_0) + F_36(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_9(x, k_0))
Eq(F_107(x, k_0), F_103(x, k_0) + F_26(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_3(x))
Eq(F_110(x, k_0), F_108(x, k_0) + F_44(x, k_0))
Eq(F_111(x), F_112(x)*F_3(x))
Eq(F_112(x), F_1(x) + F_111(x) + F_15(x) + F_97(x))
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": 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": "col_placements_tracked_fusion_isolated", "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}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "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, 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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 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"tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "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": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 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]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}], "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]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"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": [0, 1], "pos": [[0, 1], [0, 1]]}], "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]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"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]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 3
Strategy pack name: point_and_col_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/243/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[5,x]+F[57,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[7,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = F[14,x]+F[46,x,k[0]]
F[14,x] = F[15,x]+F[20,x]
F[15,x] = F[16,x,1]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[19,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[3,x]
F[18,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[19,x,k[0]] = F[16,x,k[0]]*F[9,x,k[0]]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[3,x]
F[22,x] = F[15,x]+F[21,x]+F[23,x]+F[44,x]
F[23,x] = F[24,x]
F[24,x] = F[15,x]*F[25,x]*F[3,x]
F[25,x] = F[26,x]+F[36,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[27,x]*F[3,x]
F[30,x] = F[28,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]+F[35,x]
F[32,x] = 0
F[33,x] = F[3,x]*F[34,x]
F[34,x] = F[28,x]+F[31,x]
F[35,x] = F[3,x]*F[30,x]
F[36,x] = F[37,x]
F[37,x] = F[26,x]*F[3,x]*F[38,x]
F[38,x] = F[27,x]+F[39,x]
F[39,x] = F[28,x]+F[40,x]
F[40,x] = F[32,x]+F[41,x]+F[43,x]
F[41,x] = F[3,x]*F[42,x]
F[42,x] = F[28,x]+F[40,x]
F[43,x] = F[3,x]*F[39,x]
F[44,x] = F[45,x]
F[45,x] = F[25,x]*F[27,x]*F[3,x]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[14,x]*F[48,x,k[0]]*F[9,x,k[0]]
F[48,x,k[0]] = F[27,x]+F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]+F[53,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]*F[9,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[50,x,k[0]]
F[53,x,k[0]] = F[32,x]+F[54,x,k[0]]+F[56,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]*F[9,x,k[0]]
F[55,x,k[0]] = F[28,x]+F[53,x,k[0]]
F[56,x,k[0]] = F[3,x]*F[49,x,k[0]]
F[57,x] = F[14,x]*F[3,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{57}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \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_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{7}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{9}\! \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_{3}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)+F_{44}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right) F_{3}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{36}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{3}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{3}\! \left(x \right) F_{30}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{26}\! \left(x \right) F_{3}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{28}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{41}\! \left(x \right) = F_{3}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{28}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{3}\! \left(x \right) F_{39}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{25}\! \left(x \right) F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{48}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{32}\! \left(x \right)+F_{54}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{57}\! \left(x \right) = F_{14}\! \left(x \right) F_{3}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_5(x) + F_57(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_7(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), F_14(x) + F_46(x, k_0))
Eq(F_14(x), F_15(x) + F_20(x))
Eq(F_15(x), F_16(x, 1))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0) + F_19(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_3(x))
Eq(F_18(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), F_16(x, k_0)*F_9(x, k_0))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_3(x))
Eq(F_22(x), F_15(x) + F_21(x) + F_23(x) + F_44(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_15(x)*F_25(x)*F_3(x))
Eq(F_25(x), F_26(x) + F_36(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_27(x)*F_3(x))
Eq(F_30(x), F_28(x) + F_31(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_35(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_3(x)*F_34(x))
Eq(F_34(x), F_28(x) + F_31(x))
Eq(F_35(x), F_3(x)*F_30(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_26(x)*F_3(x)*F_38(x))
Eq(F_38(x), F_27(x) + F_39(x))
Eq(F_39(x), F_28(x) + F_40(x))
Eq(F_40(x), F_32(x) + F_41(x) + F_43(x))
Eq(F_41(x), F_3(x)*F_42(x))
Eq(F_42(x), F_28(x) + F_40(x))
Eq(F_43(x), F_3(x)*F_39(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_25(x)*F_27(x)*F_3(x))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_14(x)*F_48(x, k_0)*F_9(x, k_0))
Eq(F_48(x, k_0), F_27(x) + F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0) + F_53(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0)*F_9(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_50(x, k_0))
Eq(F_53(x, k_0), F_32(x) + F_54(x, k_0) + F_56(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0)*F_9(x, k_0))
Eq(F_55(x, k_0), F_28(x) + F_53(x, k_0))
Eq(F_56(x, k_0), F_3(x)*F_49(x, k_0))
Eq(F_57(x), F_14(x)*F_3(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"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_isolated", "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}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
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{"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "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, 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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "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"}}, {"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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": 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1, 2], "pos": [[0, 3], [0, 2], [0, 2], [0, 3]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 2], [0, 3], [0, 3]]}], "requirements": [[{"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, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"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, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 0]]}], "requirements": [[{"patt": [0], 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[0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0]]}], "requirements": []}, "rule_class": "Rule", 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[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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "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]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 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": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 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": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"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]]}]]}, {"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, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [1, 1]], [[2, 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": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"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]]}], [{"patt": [0], "pos": [[1, 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": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 4
Strategy pack name: col_placements_tracked_fusion_isolated_single_fusion
Tree: http://permpal.com/tree/244/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[117,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[8,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[8,x,k[0]] = F[1,x]+F[11,x]+F[12,x,k[0]]+F[14,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[8,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x] = F[3,x]*F[6,x]
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[14,x,k[0]] = F[15,x,k[0]]*F[3,x]
F[15,x,k[0]] = (F[16,x,k[0]]*k[0]-F[16,x,1])/(-1+k[0])
F[16,x,k[0]] = F[1,x]+F[102,x]+F[116,x,k[0]]+F[17,x,k[0]]+F[18,x]
F[17,x,k[0]] = F[10,x,k[0]]*F[16,x,k[0]]
F[18,x] = F[19,x]*F[3,x]
F[19,x] = F[20,x,1]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[54,x,k[0]]+F[56,x,k[0]]+F[91,x,k[0]]
F[21,x,k[0]] = F[10,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[23,x,k[0]]+F[25,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]*F[3,x]
F[24,x,k[0]] = (F[22,x,k[0]]*k[0]-F[22,x,1])/(-1+k[0])
F[25,x,k[0]] = F[26,x,k[0]]*F[3,x]
F[26,x,k[0]] = F[27,x]+F[37,x,k[0]]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[3,x]
F[31,x] = F[29,x]+F[32,x]
F[32,x] = F[33,x]+F[34,x]+F[36,x]
F[33,x] = 0
F[34,x] = F[3,x]*F[35,x]
F[35,x] = F[29,x]+F[32,x]
F[36,x] = F[3,x]*F[31,x]
F[37,x,k[0]] = F[38,x,k[0]]+F[46,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]+F[42,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[10,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[1,x]+F[39,x,k[0]]
F[42,x,k[0]] = F[33,x]+F[43,x,k[0]]+F[45,x,k[0]]
F[43,x,k[0]] = F[10,x,k[0]]*F[44,x,k[0]]
F[44,x,k[0]] = F[29,x]+F[42,x,k[0]]
F[45,x,k[0]] = F[3,x]*F[38,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[50,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[3,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[39,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = 2*F[33,x]+F[51,x,k[0]]+F[53,x,k[0]]
F[51,x,k[0]] = F[3,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[42,x,k[0]]+F[50,x,k[0]]
F[53,x,k[0]] = F[3,x]*F[46,x,k[0]]
F[54,x,k[0]] = F[3,x]*F[55,x,k[0]]
F[55,x,k[0]] = (F[20,x,k[0]]*k[0]-F[20,x,1])/(-1+k[0])
F[56,x,k[0]] = F[3,x]*F[57,x,k[0]]
F[57,x,k[0]] = F[58,x]+F[72,x,k[0]]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[28,x]+F[60,x]
F[60,x] = F[29,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[3,x]*F[60,x]
F[63,x] = F[64,x]+F[68,x]
F[64,x] = F[29,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[3,x]*F[67,x]
F[67,x] = F[29,x]+F[65,x]
F[68,x] = F[32,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[3,x]*F[71,x]
F[71,x] = F[61,x]+F[69,x]
F[72,x,k[0]] = F[73,x,k[0]]+F[82,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[78,x,k[0]]
F[74,x,k[0]] = F[39,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[10,x,k[0]]*F[77,x,k[0]]
F[77,x,k[0]] = F[29,x]+F[75,x,k[0]]
F[78,x,k[0]] = F[42,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[10,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[61,x]+F[79,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[87,x,k[0]]
F[83,x,k[0]] = F[47,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[3,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[75,x,k[0]]+F[84,x,k[0]]
F[87,x,k[0]] = F[50,x,k[0]]+F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[3,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[79,x,k[0]]+F[88,x,k[0]]
F[91,x,k[0]] = F[3,x]*F[92,x,k[0]]
F[92,x,k[0]] = F[1,x]+F[102,x]+F[18,x]+F[91,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[10,x,k[0]]*F[41,x,k[0]]*F[95,x]
F[95,x] = F[1,x]+F[101,x]+F[96,x]
F[96,x] = F[97,x,1]
F[97,x,k[0]] = F[3,x]*F[98,x,k[0]]
F[98,x,k[0]] = 1/(-1+k[0])*(F[99,x,k[0]]*k[0]-F[99,x,1])
F[99,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[97,x,k[0]]
F[100,x,k[0]] = F[10,x,k[0]]*F[99,x,k[0]]
F[101,x] = F[100,x,1]
F[102,x] = F[103,x,1]
F[103,x,k[0]] = F[10,x,k[0]]*F[104,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[106,x,k[0]]
F[105,x,k[0]] = F[28,x]+F[49,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[64,x]
F[107,x,k[0]] = F[108,x,k[0]]+F[113,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]+F[111,x,k[0]]+F[33,x]
F[109,x,k[0]] = F[110,x,k[0]]*F[3,x]
F[110,x,k[0]] = F[108,x,k[0]]+F[39,x,k[0]]
F[111,x,k[0]] = F[10,x,k[0]]*F[112,x,k[0]]
F[112,x,k[0]] = F[108,x,k[0]]+F[29,x]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[3,x]
F[115,x,k[0]] = F[113,x,k[0]]+F[47,x,k[0]]
F[116,x,k[0]] = F[16,x,k[0]]*F[3,x]
F[117,x] = F[118,x]*F[3,x]
F[118,x] = F[1,x]+F[102,x]+F[117,x]+F[18,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{117}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = y x
F_{11}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{102}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{18}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{3}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{56}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{3}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{3}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{36}\! \left(x \right) = F_{3}\! \left(x \right) F_{31}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{33}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = 2 F_{33}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}
F_{56}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{28}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{29}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{3}\! \left(x \right) F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{29}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{3}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{29}\! \left(x \right)+F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{32}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{3}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{61}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{39}\! \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_{10}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{75}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{61}\! \left(x \right)+F_{79}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{102}\! \left(x \right)+F_{18}\! \left(x \right)+F_{91}\! \left(x , y\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_{10}\! \left(x , y\right) F_{41}\! \left(x , y\right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{1}\! \left(x \right)+F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x , 1\right)
F_{97}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = -\frac{-y F_{99}\! \left(x , y\right)+F_{99}\! \left(x , 1\right)}{-1+y}
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{101}\! \left(x \right) = F_{100}\! \left(x , 1\right)
F_{102}\! \left(x \right) = F_{103}\! \left(x , 1\right)
F_{103}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{64}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{111}\! \left(x , y\right)+F_{33}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{3}\! \left(x \right)
F_{118}\! \left(x \right) = F_{1}\! \left(x \right)+F_{102}\! \left(x \right)+F_{117}\! \left(x \right)+F_{18}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_117(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_8(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_8(x, k_0), F_1(x) + F_11(x) + F_12(x, k_0) + F_14(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_8(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x), F_3(x)*F_6(x))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_3(x))
Eq(F_15(x, k_0), (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_16(x, k_0), F_1(x) + F_102(x) + F_116(x, k_0) + F_17(x, k_0) + F_18(x))
Eq(F_17(x, k_0), F_10(x, k_0)*F_16(x, k_0))
Eq(F_18(x), F_19(x)*F_3(x))
Eq(F_19(x), F_20(x, 1))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_54(x, k_0) + F_56(x, k_0) + F_91(x, k_0))
Eq(F_21(x, k_0), F_10(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), F_1(x) + F_21(x, k_0) + F_23(x, k_0) + F_25(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0)*F_3(x))
Eq(F_24(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_3(x))
Eq(F_26(x, k_0), F_27(x) + F_37(x, k_0))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_3(x))
Eq(F_31(x), F_29(x) + F_32(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_36(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_3(x)*F_35(x))
Eq(F_35(x), F_29(x) + F_32(x))
Eq(F_36(x), F_3(x)*F_31(x))
Eq(F_37(x, k_0), F_38(x, k_0) + F_46(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0) + F_42(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_10(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_1(x) + F_39(x, k_0))
Eq(F_42(x, k_0), F_33(x) + F_43(x, k_0) + F_45(x, k_0))
Eq(F_43(x, k_0), F_10(x, k_0)*F_44(x, k_0))
Eq(F_44(x, k_0), F_29(x) + F_42(x, k_0))
Eq(F_45(x, k_0), F_3(x)*F_38(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_50(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_3(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_39(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), 2*F_33(x) + F_51(x, k_0) + F_53(x, k_0))
Eq(F_51(x, k_0), F_3(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_42(x, k_0) + F_50(x, k_0))
Eq(F_53(x, k_0), F_3(x)*F_46(x, k_0))
Eq(F_54(x, k_0), F_3(x)*F_55(x, k_0))
Eq(F_55(x, k_0), (-k_0*F_20(x, k_0) + F_20(x, 1))/(1 - k_0))
Eq(F_56(x, k_0), F_3(x)*F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x) + F_72(x, k_0))
Eq(F_58(x), F_59(x) + F_63(x))
Eq(F_59(x), F_28(x) + F_60(x))
Eq(F_60(x), F_29(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_3(x)*F_60(x))
Eq(F_63(x), F_64(x) + F_68(x))
Eq(F_64(x), F_29(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_3(x)*F_67(x))
Eq(F_67(x), F_29(x) + F_65(x))
Eq(F_68(x), F_32(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_3(x)*F_71(x))
Eq(F_71(x), F_61(x) + F_69(x))
Eq(F_72(x, k_0), F_73(x, k_0) + F_82(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_78(x, k_0))
Eq(F_74(x, k_0), F_39(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_10(x, k_0)*F_77(x, k_0))
Eq(F_77(x, k_0), F_29(x) + F_75(x, k_0))
Eq(F_78(x, k_0), F_42(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_10(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_61(x) + F_79(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_87(x, k_0))
Eq(F_83(x, k_0), F_47(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_3(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_75(x, k_0) + F_84(x, k_0))
Eq(F_87(x, k_0), F_50(x, k_0) + F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_3(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_79(x, k_0) + F_88(x, k_0))
Eq(F_91(x, k_0), F_3(x)*F_92(x, k_0))
Eq(F_92(x, k_0), F_1(x) + F_102(x) + F_18(x) + F_91(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_10(x, k_0)*F_41(x, k_0)*F_95(x))
Eq(F_95(x), F_1(x) + F_101(x) + F_96(x))
Eq(F_96(x), F_97(x, 1))
Eq(F_97(x, k_0), F_3(x)*F_98(x, k_0))
Eq(F_98(x, k_0), (k_0*F_99(x, k_0) - F_99(x, 1))/(k_0 - 1))
Eq(F_99(x, k_0), F_1(x) + F_100(x, k_0) + F_97(x, k_0))
Eq(F_100(x, k_0), F_10(x, k_0)*F_99(x, k_0))
Eq(F_101(x), F_100(x, 1))
Eq(F_102(x), F_103(x, 1))
Eq(F_103(x, k_0), F_10(x, k_0)*F_104(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_106(x, k_0))
Eq(F_105(x, k_0), F_28(x) + F_49(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_64(x))
Eq(F_107(x, k_0), F_108(x, k_0) + F_113(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0) + F_111(x, k_0) + F_33(x))
Eq(F_109(x, k_0), F_110(x, k_0)*F_3(x))
Eq(F_110(x, k_0), F_108(x, k_0) + F_39(x, k_0))
Eq(F_111(x, k_0), F_10(x, k_0)*F_112(x, k_0))
Eq(F_112(x, k_0), F_108(x, k_0) + F_29(x))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_3(x))
Eq(F_115(x, k_0), F_113(x, k_0) + F_47(x, k_0))
Eq(F_116(x, k_0), F_16(x, k_0)*F_3(x))
Eq(F_117(x), F_118(x)*F_3(x))
Eq(F_118(x), F_1(x) + F_102(x) + F_117(x) + F_18(x))
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": 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": "col_placements_tracked_fusion_isolated_single_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}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
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"rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 5
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/245/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[5,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = k[0]*x
F[5,x] = F[1,x]+F[107,x]+F[6,x]
F[6,x] = F[3,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[4,x,k[0]]*F[8,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = F[1,x]+F[106,x]+F[12,x,k[0]]+F[14,x,k[0]]+F[15,x]
F[14,x,k[0]] = F[13,x,k[0]]*F[4,x,k[0]]
F[15,x] = F[16,x]*F[3,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[51,x,k[0]]+F[53,x,k[0]]+F[94,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[4,x,k[0]]
F[19,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[20,x,k[0]]+F[22,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[3,x]
F[21,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[22,x,k[0]] = F[23,x,k[0]]*F[3,x]
F[23,x,k[0]] = F[24,x]+F[34,x,k[0]]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]*F[3,x]
F[28,x] = F[26,x]+F[29,x]
F[29,x] = F[30,x]+F[31,x]+F[33,x]
F[30,x] = 0
F[31,x] = F[3,x]*F[32,x]
F[32,x] = F[26,x]+F[29,x]
F[33,x] = F[28,x]*F[3,x]
F[34,x,k[0]] = F[35,x,k[0]]+F[43,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[39,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[4,x,k[0]]
F[38,x,k[0]] = F[1,x]+F[36,x,k[0]]
F[39,x,k[0]] = F[30,x]+F[40,x,k[0]]+F[42,x,k[0]]
F[40,x,k[0]] = F[4,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[26,x]+F[39,x,k[0]]
F[42,x,k[0]] = F[3,x]*F[35,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[3,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[36,x,k[0]]+F[44,x,k[0]]
F[47,x,k[0]] = 2*F[30,x]+F[48,x,k[0]]+F[50,x,k[0]]
F[48,x,k[0]] = F[3,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[39,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = F[3,x]*F[43,x,k[0]]
F[51,x,k[0]] = F[3,x]*F[52,x,k[0]]
F[52,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[53,x,k[0]] = F[3,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x]+F[72,x,k[0]]
F[55,x] = F[56,x,1]
F[56,x,k[0]] = F[57,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = F[25,x]+F[46,x,k[0]]
F[58,x,k[0]] = F[59,x]+F[63,x,k[0]]
F[59,x] = F[26,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[3,x]*F[62,x]
F[62,x] = F[26,x]+F[60,x]
F[63,x,k[0]] = F[64,x,k[0]]+F[69,x,k[0]]
F[64,x,k[0]] = F[30,x]+F[65,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[3,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[36,x,k[0]]+F[64,x,k[0]]
F[67,x,k[0]] = F[4,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[26,x]+F[64,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[3,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[44,x,k[0]]+F[69,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[85,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[78,x,k[0]]
F[74,x,k[0]] = F[36,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[4,x,k[0]]*F[77,x,k[0]]
F[77,x,k[0]] = F[26,x]+F[75,x,k[0]]
F[78,x,k[0]] = F[39,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[4,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[79,x,k[0]]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[3,x]*F[84,x]
F[84,x] = F[26,x]+F[82,x]
F[85,x,k[0]] = F[86,x,k[0]]+F[90,x,k[0]]
F[86,x,k[0]] = F[44,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[3,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[75,x,k[0]]+F[87,x,k[0]]
F[90,x,k[0]] = F[47,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[3,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[79,x,k[0]]+F[91,x,k[0]]
F[94,x,k[0]] = F[3,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[1,x]+F[106,x]+F[15,x]+F[94,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[97,x,k[0]]
F[97,x,k[0]] = F[38,x,k[0]]*F[4,x,k[0]]*F[98,x]
F[98,x] = F[1,x]+F[105,x]+F[99,x]
F[99,x] = F[100,x]*F[3,x]
F[100,x] = F[101,x,1]
F[101,x,k[0]] = 1/(-1+k[0])*(F[102,x,k[0]]*k[0]-F[102,x,1])
F[102,x,k[0]] = F[1,x]+F[103,x,k[0]]+F[104,x,k[0]]
F[103,x,k[0]] = F[101,x,k[0]]*F[3,x]
F[104,x,k[0]] = F[102,x,k[0]]*F[4,x,k[0]]
F[105,x] = F[3,x]*F[98,x]
F[106,x] = F[3,x]*F[55,x]
F[107,x] = F[108,x]*F[3,x]
F[108,x] = F[1,x]+F[106,x]+F[107,x]+F[15,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y\right) = y x
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{107}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{3}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{4}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{4}\! \left(x , y\right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{4}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \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_{27}\! \left(x \right) = F_{25}\! \left(x \right) F_{3}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x \right) = F_{3}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{28}\! \left(x \right) F_{3}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{4}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{4}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{53}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{55}\! \left(x \right) = F_{56}\! \left(x , 1\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{59}\! \left(x \right) = F_{26}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{3}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{26}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{4}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{36}\! \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_{4}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{75}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{4}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{3}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{26}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x \right)+F_{15}\! \left(x \right)+F_{94}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{4}\! \left(x , y\right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{105}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{3}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x , 1\right)
F_{101}\! \left(x , y\right) = -\frac{-y F_{102}\! \left(x , y\right)+F_{102}\! \left(x , 1\right)}{-1+y}
F_{102}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{4}\! \left(x , y\right)
F_{105}\! \left(x \right) = F_{3}\! \left(x \right) F_{98}\! \left(x \right)
F_{106}\! \left(x \right) = F_{3}\! \left(x \right) F_{55}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{3}\! \left(x \right)
F_{108}\! \left(x \right) = F_{1}\! \left(x \right)+F_{106}\! \left(x \right)+F_{107}\! \left(x \right)+F_{15}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_5(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), k_0*x)
Eq(F_5(x), F_1(x) + F_107(x) + F_6(x))
Eq(F_6(x), F_3(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_4(x, k_0)*F_8(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), F_1(x) + F_106(x) + F_12(x, k_0) + F_14(x, k_0) + F_15(x))
Eq(F_14(x, k_0), F_13(x, k_0)*F_4(x, k_0))
Eq(F_15(x), F_16(x)*F_3(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_51(x, k_0) + F_53(x, k_0) + F_94(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_4(x, k_0))
Eq(F_19(x, k_0), F_1(x) + F_18(x, k_0) + F_20(x, k_0) + F_22(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_3(x))
Eq(F_21(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_3(x))
Eq(F_23(x, k_0), F_24(x) + F_34(x, k_0))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_25(x)*F_3(x))
Eq(F_28(x), F_26(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_31(x) + F_33(x))
Eq(F_30(x), 0)
Eq(F_31(x), F_3(x)*F_32(x))
Eq(F_32(x), F_26(x) + F_29(x))
Eq(F_33(x), F_28(x)*F_3(x))
Eq(F_34(x, k_0), F_35(x, k_0) + F_43(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_39(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_4(x, k_0))
Eq(F_38(x, k_0), F_1(x) + F_36(x, k_0))
Eq(F_39(x, k_0), F_30(x) + F_40(x, k_0) + F_42(x, k_0))
Eq(F_40(x, k_0), F_4(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_26(x) + F_39(x, k_0))
Eq(F_42(x, k_0), F_3(x)*F_35(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_3(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_36(x, k_0) + F_44(x, k_0))
Eq(F_47(x, k_0), 2*F_30(x) + F_48(x, k_0) + F_50(x, k_0))
Eq(F_48(x, k_0), F_3(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_39(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), F_3(x)*F_43(x, k_0))
Eq(F_51(x, k_0), F_3(x)*F_52(x, k_0))
Eq(F_52(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_53(x, k_0), F_3(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x) + F_72(x, k_0))
Eq(F_55(x), F_56(x, 1))
Eq(F_56(x, k_0), F_57(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), F_25(x) + F_46(x, k_0))
Eq(F_58(x, k_0), F_59(x) + F_63(x, k_0))
Eq(F_59(x), F_26(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_3(x)*F_62(x))
Eq(F_62(x), F_26(x) + F_60(x))
Eq(F_63(x, k_0), F_64(x, k_0) + F_69(x, k_0))
Eq(F_64(x, k_0), F_30(x) + F_65(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_3(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_36(x, k_0) + F_64(x, k_0))
Eq(F_67(x, k_0), F_4(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_26(x) + F_64(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_3(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_44(x, k_0) + F_69(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_85(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_78(x, k_0))
Eq(F_74(x, k_0), F_36(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_4(x, k_0)*F_77(x, k_0))
Eq(F_77(x, k_0), F_26(x) + F_75(x, k_0))
Eq(F_78(x, k_0), F_39(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_4(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_79(x, k_0) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_3(x)*F_84(x))
Eq(F_84(x), F_26(x) + F_82(x))
Eq(F_85(x, k_0), F_86(x, k_0) + F_90(x, k_0))
Eq(F_86(x, k_0), F_44(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_3(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_75(x, k_0) + F_87(x, k_0))
Eq(F_90(x, k_0), F_47(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_3(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_79(x, k_0) + F_91(x, k_0))
Eq(F_94(x, k_0), F_3(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_1(x) + F_106(x) + F_15(x) + F_94(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_97(x, k_0))
Eq(F_97(x, k_0), F_38(x, k_0)*F_4(x, k_0)*F_98(x))
Eq(F_98(x), F_1(x) + F_105(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_3(x))
Eq(F_100(x), F_101(x, 1))
Eq(F_101(x, k_0), (k_0*F_102(x, k_0) - F_102(x, 1))/(k_0 - 1))
Eq(F_102(x, k_0), F_1(x) + F_103(x, k_0) + F_104(x, k_0))
Eq(F_103(x, k_0), F_101(x, k_0)*F_3(x))
Eq(F_104(x, k_0), F_102(x, k_0)*F_4(x, k_0))
Eq(F_105(x), F_3(x)*F_98(x))
Eq(F_106(x), F_3(x)*F_55(x))
Eq(F_107(x), F_108(x)*F_3(x))
Eq(F_108(x), F_1(x) + F_106(x) + F_107(x) + F_15(x))
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": 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": "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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "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, 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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "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"}}, {"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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"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": [], "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": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"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, 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": [[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, 0], [0, 2], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 2], [0, 2], [0, 3]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 2], [0, 3], [0, 3]]}], "requirements": [[{"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, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"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, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 0]]}], "requirements": [[{"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, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "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": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [2, 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