01234_01243_01324
Counting sequence:
1, 1, 2, 6, 24, 117, 653, 4010, 26427, 183888, 1335999, 10053592, 77894889, 618573774, 5016772752, 41436064115, 347743524509, 2959712899167, 25507701498220, 222307297239388, 1957097426070754, 17387325476791641, 155760310784168788, 1405961415464106157, 12779398695474756043, 116903731898178871861, 1075760032259113938871, 9953667970561688239258, 92568533938071499551761, 864978350923448821214736, 8118445184766684837040784, 76514457815234732742229643, 723945481958655368464830192, 6874778242735425360247854969, 65510307983514497677314480853, 626288174453234938681445886435, 6005855874047165706275537511650, 57761766368819762311207225003185, 557064156797253346639712047308978, 5386522699240246127669406444465594, 52214864371226186485674435889346278, 507352871207510581651917717292899662, 4940922189487852638593860292631949335, 48221730664240907587562020228907381770, 471598553233321296232900084519639977836, 4621232392141973512145011573411621948054, 45369306712743483961716895138582365275206, 446222126918393301820054295338363100672607, 4396351919201420734088914492507598225072190, 43386628614031008162818031902948310795837105, 428857475182371660995287288171181536970067480, 4245578423170083417774247636034168190966649171, 42092261848879742530725733305765954484231169884, 417912440827177138281294294980195089464604654359, 4154927188543906174839535136838913573061501728881, 41363309129671329918751527999627603076010240874127, 412306959401193039198757664518735481589546416128710, 4114910850874619177785072845048512225870397611536221, 41116524423897025921824443610464821926667604164670928, 411311927051033478807365192014560759436282790900519073, 4119160786757217045733952820563368725871832778357341360, 41296487449218930260533480408285051985397296291025368464, 414447525230198993745946941623215881763904690299573356113, 4163551079199043583268868745685401173119452393650918995429, 41868041926084441171392349647980787804429977546065859518244, 421417848520391230628606713702719234546372156103889647728644, 4245632675049577835619936256338252553594153007859539985229318, 42811393551098088706289731264872386612732181349994867912128766, 432068417469103829156800795805228012347533269442717495883153116, 4364265137539145991442765337064447365448068449857666626389630781, 44118920035107134004051912720407183568789976775114935014238714783, 446358578260241962159810759275921383509262911309912116725473566388, 4519378311714061306601894188643601831844126902143711590826625567581, 45793119058817385299468734040517100656483868831575501032857472035041, 464343907688554024361680848405188343885943462467915113459047615836512, 4711822313141185901241964019173646724318056183632488702207477794788682, 47845339156529951785425834188196487908726189945752337859649566432060198, 486165588555750937254271315855442408451060214915931053708493596408804191, 4943279859440851083303125468181690938065589208501664427291153606845683962, 50295070891833966699101570998281791120907115153703804668383208530790545955, 512044846358509556313220835142435786766404856699179495528019491934962233308, 5216224569464386343740993892349425582235268119192000155287267497836812865229, 53169657903120851191832070260627454072658575709367753569371525666151376621522, 542281244092645197553112608783371436989381547834403370976281703595738690725794, 5533914936763336511678440977492508730986497165850848823000900204706008224091424, 56504339970113748446475568424651686808454665183935058135356526843806358606733325, 577254088065137339912587368050271984027120172563213036929212411166155135969066529, 5900417654985316258713317398705881266185665149145695100783728828596022579498756896, 60342574963273574943070201428261699456902252994918234176893170697679898235714201336, 617426502273971843993828111141469975098701708596834537047182412102032580693324235314, 6320656658873213221201536776548064686802965397972870560064020831594761235212215746537, 64736610331374470026532015711887593925791566604311024895208464987474198191621415808908, 663351940758155781443626147862322261312219279730957106919410132546381039741654450111755, 6800486141014450185730489863611021539545771245809075846997472929833306529371365107165021, 69748291860353383870636788315881887231218282721626596327005623637356832338989847938520911, 715683062078244707294160197421651622806905998109569242646829742158444710121331308608185076, 7346787216341129448154403614138216277060463359009139514918460606297791909346945750845852898, 75450110408835561896727172741134056155591811362069677217477637529427512850329378939822008522, 775183010174149665583000487514127866379424201972563952303413877066462876765140437128950037726, 7967589026742464496557721123677373041645762008642460806406553085076928103223755418687937321792, 81926497862684667749823428961199111240082095262037266229145096252458650403261643308960638653128
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24423/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[42,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[35,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[12,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,1,k[0]]
F[9,x,k[0],k[1]] = F[10,x,k[0]*k[1],k[1]]
F[10,x,k[0],k[1]] = F[1,x]+F[11,x,k[0],k[1]]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[11,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[12,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0],k[1]] = F[12,x,k[1]]*F[14,x,k[0],k[1]]
F[14,x,k[0],k[1]] = (-F[9,x,1,k[1]]*k[1]+F[9,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[21,x]
F[16,x,k[0],k[1]] = (F[17,x,k[0]]*k[0]-F[17,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[19,x,k[0]]+F[22,x,k[0]]+F[23,x,k[0]]
F[18,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x]
F[20,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[21,x] = x
F[22,x,k[0]] = F[20,x,k[0]]*F[21,x]
F[23,x,k[0]] = F[21,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0],1]
F[25,x,k[0],k[1]] = (F[26,x,k[0],k[1]]*k[1]-F[26,x,k[0],1])/(-1+k[1])
F[26,x,k[0],k[1]] = F[1,x]+F[27,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[12,x,k[0]]*F[26,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[12,x,k[1]]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = (-F[30,x,1,k[1]]*k[1]+F[30,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[30,x,k[0],k[1]] = F[26,x,k[0]*k[1],k[1]]
F[31,x,k[0],k[1]] = F[21,x]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[10,x,k[0],k[1]]*k[1]-F[10,x,k[0],1])/(-1+k[1])
F[33,x,k[0],k[1]] = F[21,x]*F[25,x,k[0],k[1]]
F[34,x,k[0]] = F[17,x,k[0]]*F[21,x]
F[35,x,k[0]] = F[21,x]*F[36,x,k[0]]
F[36,x,k[0]] = (F[37,x,k[0]]*k[0]-F[37,x,1])/(-1+k[0])
F[37,x,k[0]] = F[1,x]+F[35,x,k[0]]+F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[12,x,k[0]]*F[39,x,k[0]]
F[39,x,k[0]] = F[30,x,1,k[0]]
F[40,x,k[0]] = F[21,x]*F[41,x,k[0]]
F[41,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[42,x] = F[21,x]*F[43,x]
F[43,x] = F[37,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , 1, y\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y z , z\right)
F_{10}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{11}\! \left(x , y , z\right) = F_{10}\! \left(x , y , z\right) F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = y x
F_{13}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{14}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = -\frac{F_{9}\! \left(x , 1, z\right) z -F_{9}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{21}\! \left(x \right)
F_{16}\! \left(x , y , z\right) = \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , z\right) z}{-z +y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y , 1\right)
F_{25}\! \left(x , y , z\right) = -\frac{-F_{26}\! \left(x , y , z\right) z +F_{26}\! \left(x , y , 1\right)}{-1+z}
F_{26}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{28}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{26}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{29}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = -\frac{F_{30}\! \left(x , 1, z\right) z -F_{30}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{30}\! \left(x , y , z\right) = F_{26}\! \left(x , y z , z\right)
F_{31}\! \left(x , y , z\right) = F_{21}\! \left(x \right) F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = -\frac{-F_{10}\! \left(x , y , z\right) z +F_{10}\! \left(x , y , 1\right)}{-1+z}
F_{33}\! \left(x , y , z\right) = F_{21}\! \left(x \right) F_{25}\! \left(x , y , z\right)
F_{34}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-F_{37}\! \left(x , y\right) y +F_{37}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x , 1, y\right)
F_{40}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{42}\! \left(x \right) = F_{21}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_42(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_34(x, k_0) + F_35(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_12(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, 1, k_0))
Eq(F_9(x, k_0, k_1), F_10(x, k_0*k_1, k_1))
Eq(F_10(x, k_0, k_1), F_1(x) + F_11(x, k_0, k_1) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_11(x, k_0, k_1), F_10(x, k_0, k_1)*F_12(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0, k_1), F_12(x, k_1)*F_14(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), (-k_0*F_9(x, k_0/k_1, k_1) + k_1*F_9(x, 1, k_1))/(-k_0 + k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_21(x))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0) + k_1*F_17(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_19(x, k_0) + F_22(x, k_0) + F_23(x, k_0))
Eq(F_18(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x))
Eq(F_20(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_21(x), x)
Eq(F_22(x, k_0), F_20(x, k_0)*F_21(x))
Eq(F_23(x, k_0), F_21(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0, 1))
Eq(F_25(x, k_0, k_1), (-k_1*F_26(x, k_0, k_1) + F_26(x, k_0, 1))/(1 - k_1))
Eq(F_26(x, k_0, k_1), F_1(x) + F_27(x, k_0, k_1) + F_28(x, k_0, k_1) + F_31(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_12(x, k_0)*F_26(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_12(x, k_1)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (-k_0*F_30(x, k_0/k_1, k_1) + k_1*F_30(x, 1, k_1))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1), F_26(x, k_0*k_1, k_1))
Eq(F_31(x, k_0, k_1), F_21(x)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_1*F_10(x, k_0, k_1) + F_10(x, k_0, 1))/(1 - k_1))
Eq(F_33(x, k_0, k_1), F_21(x)*F_25(x, k_0, k_1))
Eq(F_34(x, k_0), F_17(x, k_0)*F_21(x))
Eq(F_35(x, k_0), F_21(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (-k_0*F_37(x, k_0) + F_37(x, 1))/(1 - k_0))
Eq(F_37(x, k_0), F_1(x) + F_35(x, k_0) + F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_12(x, k_0)*F_39(x, k_0))
Eq(F_39(x, k_0), F_30(x, 1, k_0))
Eq(F_40(x, k_0), F_21(x)*F_41(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_42(x), F_21(x)*F_43(x))
Eq(F_43(x), F_37(x, 1))
Pack JSON:
{"name": "row_and_col_placements_tracked_fusion_expand_verified", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.sliding", "strategy_class": "SlidingFactory", "use_symmetries": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
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4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: all_the_strategies_2_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24809/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[18,x]*F[4,x]
F[4,x] = F[1,x]+F[32,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[18,x]*F[7,x,k[0]]
F[7,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[27,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,1,k[0]]
F[9,x,k[0],k[1]] = F[10,x,k[0]*k[1],k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[13,x,k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[19,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[13,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0],k[1]] = (-F[9,x,1,k[1]]*k[1]+F[9,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[15,x,k[0],k[1]] = (F[16,x,k[0]]*k[0]-F[16,x,k[1]]*k[1])/(-k[1]+k[0])
F[16,x,k[0]] = F[17,x,k[0],1]
F[17,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[18,x]
F[18,x] = x
F[19,x,k[0],k[1]] = (F[20,x,k[0],k[1]]*k[1]-F[20,x,k[0],1])/(-1+k[1])
F[20,x,k[0],k[1]] = F[18,x]*F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[1,x]+F[19,x,k[0],k[1]]+F[22,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[26,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[13,x,k[0]]*F[21,x,k[0],k[1]]
F[23,x,k[0],k[1]] = (-F[24,x,1,k[1]]*k[1]+F[24,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1]] = F[25,x,k[0]*k[1],k[1]]
F[25,x,k[0],k[1]] = F[13,x,k[1]]*F[21,x,k[0],k[1]]
F[26,x,k[0],k[1]] = (F[17,x,k[0],k[1]]*k[1]-F[17,x,k[0],1])/(-1+k[1])
F[27,x,k[0]] = (F[28,x,k[0]]*k[0]-F[28,x,1])/(-1+k[0])
F[28,x,k[0]] = F[18,x]*F[29,x,k[0]]
F[29,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[30,x,k[0]]+F[31,x,k[0]]
F[30,x,k[0]] = F[24,x,1,k[0]]
F[31,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[32,x] = F[28,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , 1, y\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y z , z\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right) F_{13}\! \left(x , z\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{19}\! \left(x , y , z\right)
F_{12}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x , y , z\right) = -\frac{F_{9}\! \left(x , 1, z\right) z -F_{9}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{15}\! \left(x , y , z\right) = \frac{F_{16}\! \left(x , y\right) y -F_{16}\! \left(x , z\right) z}{-z +y}
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y , 1\right)
F_{17}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x , y , z\right) = -\frac{-F_{20}\! \left(x , y , z\right) z +F_{20}\! \left(x , y , 1\right)}{-1+z}
F_{20}\! \left(x , y , z\right) = F_{18}\! \left(x \right) F_{21}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = -\frac{F_{24}\! \left(x , 1, z\right) z -F_{24}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y z , z\right)
F_{25}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{21}\! \left(x , y , z\right)
F_{26}\! \left(x , y , z\right) = -\frac{-z F_{17}\! \left(x , y , z\right)+F_{17}\! \left(x , y , 1\right)}{-1+z}
F_{27}\! \left(x , y\right) = -\frac{-F_{28}\! \left(x , y\right) y +F_{28}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{24}\! \left(x , 1, y\right)
F_{31}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x \right) = F_{28}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_32(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_18(x)*F_7(x, k_0))
Eq(F_7(x, k_0), F_1(x) + F_16(x, k_0) + F_27(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, 1, k_0))
Eq(F_9(x, k_0, k_1), F_10(x, k_0*k_1, k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0, k_1)*F_13(x, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1) + F_15(x, k_0, k_1) + F_19(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_11(x, k_0, k_1)*F_13(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0, k_1), (-k_0*F_9(x, k_0/k_1, k_1) + k_1*F_9(x, 1, k_1))/(-k_0 + k_1))
Eq(F_15(x, k_0, k_1), (-k_0*F_16(x, k_0) + k_1*F_16(x, k_1))/(-k_0 + k_1))
Eq(F_16(x, k_0), F_17(x, k_0, 1))
Eq(F_17(x, k_0, k_1), F_11(x, k_0, k_1)*F_18(x))
Eq(F_18(x), x)
Eq(F_19(x, k_0, k_1), (-k_1*F_20(x, k_0, k_1) + F_20(x, k_0, 1))/(1 - k_1))
Eq(F_20(x, k_0, k_1), F_18(x)*F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_1(x) + F_19(x, k_0, k_1) + F_22(x, k_0, k_1) + F_23(x, k_0, k_1) + F_26(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_13(x, k_0)*F_21(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), (-k_0*F_24(x, k_0/k_1, k_1) + k_1*F_24(x, 1, k_1))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0*k_1, k_1))
Eq(F_25(x, k_0, k_1), F_13(x, k_1)*F_21(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), (-k_1*F_17(x, k_0, k_1) + F_17(x, k_0, 1))/(1 - k_1))
Eq(F_27(x, k_0), (-k_0*F_28(x, k_0) + F_28(x, 1))/(1 - k_0))
Eq(F_28(x, k_0), F_18(x)*F_29(x, k_0))
Eq(F_29(x, k_0), F_1(x) + F_27(x, k_0) + F_30(x, k_0) + F_31(x, k_0))
Eq(F_30(x, k_0), F_24(x, 1, k_0))
Eq(F_31(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_32(x), F_28(x, 1))
Pack JSON:
{"name": "all_the_strategies_2_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionFactory", "ignore_parent": false, "maxreqlen": 2, "extra_basis": [], "limited_insertion": true, "allow_factorable_insertions": true}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "AllPlacementsFactory", "ignore_parent": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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"comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [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": [[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, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 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[[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 0, "own_col": true, "own_row": true, "include_empty": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 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"TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 1, "col_idx": null, "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], 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0], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/25220/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[42,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[35,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[12,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,1,k[0]]
F[9,x,k[0],k[1]] = F[10,x,k[0]*k[1],k[1]]
F[10,x,k[0],k[1]] = F[1,x]+F[11,x,k[0],k[1]]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[11,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[12,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0],k[1]] = F[12,x,k[1]]*F[14,x,k[0],k[1]]
F[14,x,k[0],k[1]] = (-F[9,x,1,k[1]]*k[1]+F[9,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[21,x]
F[16,x,k[0],k[1]] = (F[17,x,k[0]]*k[0]-F[17,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[19,x,k[0]]+F[22,x,k[0]]+F[23,x,k[0]]
F[18,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x]
F[20,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[21,x] = x
F[22,x,k[0]] = F[20,x,k[0]]*F[21,x]
F[23,x,k[0]] = F[21,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0],1]
F[25,x,k[0],k[1]] = (F[26,x,k[0],k[1]]*k[1]-F[26,x,k[0],1])/(-1+k[1])
F[26,x,k[0],k[1]] = F[1,x]+F[27,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[12,x,k[0]]*F[26,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[12,x,k[1]]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = (-F[30,x,1,k[1]]*k[1]+F[30,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[30,x,k[0],k[1]] = F[26,x,k[0]*k[1],k[1]]
F[31,x,k[0],k[1]] = F[21,x]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[10,x,k[0],k[1]]*k[1]-F[10,x,k[0],1])/(-1+k[1])
F[33,x,k[0],k[1]] = F[21,x]*F[25,x,k[0],k[1]]
F[34,x,k[0]] = F[17,x,k[0]]*F[21,x]
F[35,x,k[0]] = F[21,x]*F[36,x,k[0]]
F[36,x,k[0]] = (F[37,x,k[0]]*k[0]-F[37,x,1])/(-1+k[0])
F[37,x,k[0]] = F[1,x]+F[35,x,k[0]]+F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[12,x,k[0]]*F[39,x,k[0]]
F[39,x,k[0]] = F[30,x,1,k[0]]
F[40,x,k[0]] = F[21,x]*F[41,x,k[0]]
F[41,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[42,x] = F[21,x]*F[43,x]
F[43,x] = F[37,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , 1, y\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y z , z\right)
F_{10}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{11}\! \left(x , y , z\right) = F_{10}\! \left(x , y , z\right) F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = y x
F_{13}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{14}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = -\frac{F_{9}\! \left(x , 1, z\right) z -F_{9}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{21}\! \left(x \right)
F_{16}\! \left(x , y , z\right) = \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , z\right) z}{-z +y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y , 1\right)
F_{25}\! \left(x , y , z\right) = -\frac{-F_{26}\! \left(x , y , z\right) z +F_{26}\! \left(x , y , 1\right)}{-1+z}
F_{26}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{28}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{26}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{29}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = -\frac{F_{30}\! \left(x , 1, z\right) z -F_{30}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{30}\! \left(x , y , z\right) = F_{26}\! \left(x , y z , z\right)
F_{31}\! \left(x , y , z\right) = F_{21}\! \left(x \right) F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = -\frac{-F_{10}\! \left(x , y , z\right) z +F_{10}\! \left(x , y , 1\right)}{-1+z}
F_{33}\! \left(x , y , z\right) = F_{21}\! \left(x \right) F_{25}\! \left(x , y , z\right)
F_{34}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-F_{37}\! \left(x , y\right) y +F_{37}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x , 1, y\right)
F_{40}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{42}\! \left(x \right) = F_{21}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_42(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_34(x, k_0) + F_35(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_12(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, 1, k_0))
Eq(F_9(x, k_0, k_1), F_10(x, k_0*k_1, k_1))
Eq(F_10(x, k_0, k_1), F_1(x) + F_11(x, k_0, k_1) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_11(x, k_0, k_1), F_10(x, k_0, k_1)*F_12(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0, k_1), F_12(x, k_1)*F_14(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), (-k_0*F_9(x, k_0/k_1, k_1) + k_1*F_9(x, 1, k_1))/(-k_0 + k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_21(x))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0) + k_1*F_17(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_19(x, k_0) + F_22(x, k_0) + F_23(x, k_0))
Eq(F_18(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x))
Eq(F_20(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_21(x), x)
Eq(F_22(x, k_0), F_20(x, k_0)*F_21(x))
Eq(F_23(x, k_0), F_21(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0, 1))
Eq(F_25(x, k_0, k_1), (-k_1*F_26(x, k_0, k_1) + F_26(x, k_0, 1))/(1 - k_1))
Eq(F_26(x, k_0, k_1), F_1(x) + F_27(x, k_0, k_1) + F_28(x, k_0, k_1) + F_31(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_12(x, k_0)*F_26(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_12(x, k_1)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (-k_0*F_30(x, k_0/k_1, k_1) + k_1*F_30(x, 1, k_1))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1), F_26(x, k_0*k_1, k_1))
Eq(F_31(x, k_0, k_1), F_21(x)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_1*F_10(x, k_0, k_1) + F_10(x, k_0, 1))/(1 - k_1))
Eq(F_33(x, k_0, k_1), F_21(x)*F_25(x, k_0, k_1))
Eq(F_34(x, k_0), F_17(x, k_0)*F_21(x))
Eq(F_35(x, k_0), F_21(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (-k_0*F_37(x, k_0) + F_37(x, 1))/(1 - k_0))
Eq(F_37(x, k_0), F_1(x) + F_35(x, k_0) + F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_12(x, k_0)*F_39(x, k_0))
Eq(F_39(x, k_0), F_30(x, 1, k_0))
Eq(F_40(x, k_0), F_21(x)*F_41(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_42(x), F_21(x)*F_43(x))
Eq(F_43(x), F_37(x, 1))
Pack JSON:
{"name": "row_and_col_placements_tracked_fusion_req_corrob_expand_verified", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.sliding", "strategy_class": "SlidingFactory", "use_symmetries": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
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4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 4
Strategy pack name: row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/25278/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[42,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[35,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[12,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,1,k[0]]
F[9,x,k[0],k[1]] = F[10,x,k[0]*k[1],k[1]]
F[10,x,k[0],k[1]] = F[1,x]+F[11,x,k[0],k[1]]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[11,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[12,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0],k[1]] = F[12,x,k[1]]*F[14,x,k[0],k[1]]
F[14,x,k[0],k[1]] = (-F[9,x,1,k[1]]*k[1]+F[9,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[21,x]
F[16,x,k[0],k[1]] = (F[17,x,k[0]]*k[0]-F[17,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[19,x,k[0]]+F[22,x,k[0]]+F[23,x,k[0]]
F[18,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x]
F[20,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[21,x] = x
F[22,x,k[0]] = F[20,x,k[0]]*F[21,x]
F[23,x,k[0]] = F[21,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0],1]
F[25,x,k[0],k[1]] = (F[26,x,k[0],k[1]]*k[1]-F[26,x,k[0],1])/(-1+k[1])
F[26,x,k[0],k[1]] = F[1,x]+F[27,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[12,x,k[0]]*F[26,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[12,x,k[1]]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = (-F[30,x,1,k[1]]*k[1]+F[30,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[30,x,k[0],k[1]] = F[26,x,k[0]*k[1],k[1]]
F[31,x,k[0],k[1]] = F[21,x]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[10,x,k[0],k[1]]*k[1]-F[10,x,k[0],1])/(-1+k[1])
F[33,x,k[0],k[1]] = F[21,x]*F[25,x,k[0],k[1]]
F[34,x,k[0]] = F[17,x,k[0]]*F[21,x]
F[35,x,k[0]] = F[21,x]*F[36,x,k[0]]
F[36,x,k[0]] = (F[37,x,k[0]]*k[0]-F[37,x,1])/(-1+k[0])
F[37,x,k[0]] = F[1,x]+F[35,x,k[0]]+F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[12,x,k[0]]*F[39,x,k[0]]
F[39,x,k[0]] = F[30,x,1,k[0]]
F[40,x,k[0]] = F[21,x]*F[41,x,k[0]]
F[41,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[42,x] = F[21,x]*F[43,x]
F[43,x] = F[37,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , 1, y\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y z , z\right)
F_{10}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{11}\! \left(x , y , z\right) = F_{10}\! \left(x , y , z\right) F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = y x
F_{13}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{14}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = -\frac{F_{9}\! \left(x , 1, z\right) z -F_{9}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{21}\! \left(x \right)
F_{16}\! \left(x , y , z\right) = \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , z\right) z}{-z +y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y , 1\right)
F_{25}\! \left(x , y , z\right) = -\frac{-F_{26}\! \left(x , y , z\right) z +F_{26}\! \left(x , y , 1\right)}{-1+z}
F_{26}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{28}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{26}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{29}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = -\frac{F_{30}\! \left(x , 1, z\right) z -F_{30}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{30}\! \left(x , y , z\right) = F_{26}\! \left(x , y z , z\right)
F_{31}\! \left(x , y , z\right) = F_{21}\! \left(x \right) F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = -\frac{-F_{10}\! \left(x , y , z\right) z +F_{10}\! \left(x , y , 1\right)}{-1+z}
F_{33}\! \left(x , y , z\right) = F_{21}\! \left(x \right) F_{25}\! \left(x , y , z\right)
F_{34}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-F_{37}\! \left(x , y\right) y +F_{37}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x , 1, y\right)
F_{40}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{42}\! \left(x \right) = F_{21}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_42(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_34(x, k_0) + F_35(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_12(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, 1, k_0))
Eq(F_9(x, k_0, k_1), F_10(x, k_0*k_1, k_1))
Eq(F_10(x, k_0, k_1), F_1(x) + F_11(x, k_0, k_1) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_11(x, k_0, k_1), F_10(x, k_0, k_1)*F_12(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0, k_1), F_12(x, k_1)*F_14(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), (-k_0*F_9(x, k_0/k_1, k_1) + k_1*F_9(x, 1, k_1))/(-k_0 + k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_21(x))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0) + k_1*F_17(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_19(x, k_0) + F_22(x, k_0) + F_23(x, k_0))
Eq(F_18(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x))
Eq(F_20(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_21(x), x)
Eq(F_22(x, k_0), F_20(x, k_0)*F_21(x))
Eq(F_23(x, k_0), F_21(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0, 1))
Eq(F_25(x, k_0, k_1), (-k_1*F_26(x, k_0, k_1) + F_26(x, k_0, 1))/(1 - k_1))
Eq(F_26(x, k_0, k_1), F_1(x) + F_27(x, k_0, k_1) + F_28(x, k_0, k_1) + F_31(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_12(x, k_0)*F_26(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_12(x, k_1)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (-k_0*F_30(x, k_0/k_1, k_1) + k_1*F_30(x, 1, k_1))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1), F_26(x, k_0*k_1, k_1))
Eq(F_31(x, k_0, k_1), F_21(x)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_1*F_10(x, k_0, k_1) + F_10(x, k_0, 1))/(1 - k_1))
Eq(F_33(x, k_0, k_1), F_21(x)*F_25(x, k_0, k_1))
Eq(F_34(x, k_0), F_17(x, k_0)*F_21(x))
Eq(F_35(x, k_0), F_21(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (-k_0*F_37(x, k_0) + F_37(x, 1))/(1 - k_0))
Eq(F_37(x, k_0), F_1(x) + F_35(x, k_0) + F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_12(x, k_0)*F_39(x, k_0))
Eq(F_39(x, k_0), F_30(x, 1, k_0))
Eq(F_40(x, k_0), F_21(x)*F_41(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_42(x), F_21(x)*F_43(x))
Eq(F_43(x), F_37(x, 1))
Pack JSON:
{"name": "row_placements_tracked_fusion_expand_verified", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.sliding", "strategy_class": "SlidingFactory", "use_symmetries": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], 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{"patt": [0, 1, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 5
Strategy pack name: row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/25644/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[42,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[35,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[12,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,1,k[0]]
F[9,x,k[0],k[1]] = F[10,x,k[0]*k[1],k[1]]
F[10,x,k[0],k[1]] = F[1,x]+F[11,x,k[0],k[1]]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[11,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[12,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0],k[1]] = F[12,x,k[1]]*F[14,x,k[0],k[1]]
F[14,x,k[0],k[1]] = (-F[9,x,1,k[1]]*k[1]+F[9,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[21,x]
F[16,x,k[0],k[1]] = (F[17,x,k[0]]*k[0]-F[17,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[19,x,k[0]]+F[22,x,k[0]]+F[23,x,k[0]]
F[18,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x]
F[20,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[21,x] = x
F[22,x,k[0]] = F[20,x,k[0]]*F[21,x]
F[23,x,k[0]] = F[21,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0],1]
F[25,x,k[0],k[1]] = (F[26,x,k[0],k[1]]*k[1]-F[26,x,k[0],1])/(-1+k[1])
F[26,x,k[0],k[1]] = F[1,x]+F[27,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[12,x,k[0]]*F[26,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[12,x,k[1]]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = (-F[30,x,1,k[1]]*k[1]+F[30,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[30,x,k[0],k[1]] = F[26,x,k[0]*k[1],k[1]]
F[31,x,k[0],k[1]] = F[21,x]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[10,x,k[0],k[1]]*k[1]-F[10,x,k[0],1])/(-1+k[1])
F[33,x,k[0],k[1]] = F[21,x]*F[25,x,k[0],k[1]]
F[34,x,k[0]] = F[17,x,k[0]]*F[21,x]
F[35,x,k[0]] = F[21,x]*F[36,x,k[0]]
F[36,x,k[0]] = (F[37,x,k[0]]*k[0]-F[37,x,1])/(-1+k[0])
F[37,x,k[0]] = F[1,x]+F[35,x,k[0]]+F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[12,x,k[0]]*F[39,x,k[0]]
F[39,x,k[0]] = F[30,x,1,k[0]]
F[40,x,k[0]] = F[21,x]*F[41,x,k[0]]
F[41,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[42,x] = F[21,x]*F[43,x]
F[43,x] = F[37,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , 1, y\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y z , z\right)
F_{10}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{11}\! \left(x , y , z\right) = F_{10}\! \left(x , y , z\right) F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = y x
F_{13}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{14}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = -\frac{F_{9}\! \left(x , 1, z\right) z -F_{9}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{21}\! \left(x \right)
F_{16}\! \left(x , y , z\right) = \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , z\right) z}{-z +y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y , 1\right)
F_{25}\! \left(x , y , z\right) = -\frac{-F_{26}\! \left(x , y , z\right) z +F_{26}\! \left(x , y , 1\right)}{-1+z}
F_{26}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{28}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{26}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{29}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = -\frac{F_{30}\! \left(x , 1, z\right) z -F_{30}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{30}\! \left(x , y , z\right) = F_{26}\! \left(x , y z , z\right)
F_{31}\! \left(x , y , z\right) = F_{21}\! \left(x \right) F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = -\frac{-F_{10}\! \left(x , y , z\right) z +F_{10}\! \left(x , y , 1\right)}{-1+z}
F_{33}\! \left(x , y , z\right) = F_{21}\! \left(x \right) F_{25}\! \left(x , y , z\right)
F_{34}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-F_{37}\! \left(x , y\right) y +F_{37}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x , 1, y\right)
F_{40}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{42}\! \left(x \right) = F_{21}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_42(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_34(x, k_0) + F_35(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_12(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, 1, k_0))
Eq(F_9(x, k_0, k_1), F_10(x, k_0*k_1, k_1))
Eq(F_10(x, k_0, k_1), F_1(x) + F_11(x, k_0, k_1) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_11(x, k_0, k_1), F_10(x, k_0, k_1)*F_12(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0, k_1), F_12(x, k_1)*F_14(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), (-k_0*F_9(x, k_0/k_1, k_1) + k_1*F_9(x, 1, k_1))/(-k_0 + k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_21(x))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0) + k_1*F_17(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_19(x, k_0) + F_22(x, k_0) + F_23(x, k_0))
Eq(F_18(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x))
Eq(F_20(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_21(x), x)
Eq(F_22(x, k_0), F_20(x, k_0)*F_21(x))
Eq(F_23(x, k_0), F_21(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0, 1))
Eq(F_25(x, k_0, k_1), (-k_1*F_26(x, k_0, k_1) + F_26(x, k_0, 1))/(1 - k_1))
Eq(F_26(x, k_0, k_1), F_1(x) + F_27(x, k_0, k_1) + F_28(x, k_0, k_1) + F_31(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_12(x, k_0)*F_26(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_12(x, k_1)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (-k_0*F_30(x, k_0/k_1, k_1) + k_1*F_30(x, 1, k_1))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1), F_26(x, k_0*k_1, k_1))
Eq(F_31(x, k_0, k_1), F_21(x)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_1*F_10(x, k_0, k_1) + F_10(x, k_0, 1))/(1 - k_1))
Eq(F_33(x, k_0, k_1), F_21(x)*F_25(x, k_0, k_1))
Eq(F_34(x, k_0), F_17(x, k_0)*F_21(x))
Eq(F_35(x, k_0), F_21(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (-k_0*F_37(x, k_0) + F_37(x, 1))/(1 - k_0))
Eq(F_37(x, k_0), F_1(x) + F_35(x, k_0) + F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_12(x, k_0)*F_39(x, k_0))
Eq(F_39(x, k_0), F_30(x, 1, k_0))
Eq(F_40(x, k_0), F_21(x)*F_41(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_42(x), F_21(x)*F_43(x))
Eq(F_43(x), F_37(x, 1))
Pack JSON:
{"name": "row_placements_tracked_fusion_req_corrob_expand_verified", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.sliding", "strategy_class": "SlidingFactory", "use_symmetries": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 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