01234_01243_01342_02134_02143_02341_03124_03142_03241_04123_04132_04231<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 24, 108, 512, 2498, 12410, 62410, 316576, 1615962, 8287620, 42657584, 220184686, 1139068350, 5903296104, 30639130652, 159214569482, 828180601878, 4311541554800, 22462004362692, 117091830577516, 610701363646246, 3186573921462074, 16633581222489538, 86854484514107972, 453654197305871838, 2370107843874686820, 12385352245321407240, 64734262598500139524, 338404195151444255738, 1769311921796870901930, 9251939262070723430826, 48385404236070280898884, 253071680059338323622698, 1323778535801034545952432, 6925089171320009238365028, 36230122616742189468544000, 189559359378543845192741030, 991856028098724057134850270, 5190119244560396611618681710, 27159948360582435131553861760, 142135092458961376250959757390, 743862316577954579474724351660, 3893148383801095259298804671280, 20376283655368012776414858850150, 106650584937096703217787400605770, 558231714511643842565337207955140, 2921982766695413337926506301315160, 15295076768353859150786550800792386, 80063693779207493185125625341658082, 419110657546530393913513217265880320, 2193967318765082588664738843270427404, 11485219162935874678417348866385892756, 60125054230011131974053452803794400058, 314759009756920007386796670394145598710, 1647808878101725035297706282159344933262, 8626626882677695749862839144564268103164, 45162738510354793459911262384729301492706, 236441772482643408481918280163975269234756, 1237862678647095308197665012836591833792016, 6480741920870316499385962553285175223674302, 33929751421507153090666541605691228177496686, 177639705436127080391583194553969302898228264, 930042022535767476606349843915506396057363580, 4869316753711993329890888059485237675553723306, 25493895051085768497746222794828815225636757798, 133477134528561805404468732242206464725937301488, 698843431548969344246222171512816775315493154852, 3658938115785188093913334551234776540897082479920, 19157209551143616876244453581646248362449555614118, 100302394555927067742546124497597897293502002008094, 525160540339744242115653632850052842667543445480494, 2749631431725090978995182927927935177188190296312336, 14396548346140488237979520723729467584218452172725230, 75377837032748003527561145773889447575779668449661964, 394666496808995976195124466769304324304609966022780432, 2066417443705621039382498173604700289514361618034091642, 10819494837494208562882656176213011130114229606543651578, 56649614420838483000727743353032133897955211816357601960, 296611449190844291117639536504179337557747492654746565412, 1553029751479154410653129856010178694116880345374405557806, 8131534173516203028795339285834359252700861991525301063106, 42576112185176459278662857638994579629025994006737819798544, 222925758447184912488746128199197548713715140611300528340300, 1167226654451514044795938470620357253072842893828894026154516, 6111541800022351618507019949871850002005389231381686175378898, 31999779118548104166732459374112083499879040605281799196090398, 167549732652236911417113363585720386634660860890381165324369622, 877285650042245418964229476767958651699910572528608012681129340, 4593448011638329342240972844722658296601254749581806366157502138, 24051216454080976097925890370571602345027013662307483659606975804, 125931889653815546935143617585426953823922968635891073186583129224, 659378523322774556676098357809862066191775065727255747048404199896, 3452504500187095174667172662153492867924165090289021556635348348510, 18077320725206816795059671470869961518764087963263841751705579815114, 94652961115438619530242734343134659680131160488635820772831083064962, 495603833903009912378856310824738726025456843443681618947286778551712, 2594988280815596696495251801293614587146846901019218906122635504533278, 13587401766308091247400797800956420913974042476941035633004699544462320<br /><br />


















  Specification 1<br />
  Strategy pack name: col_placements_tracked_fusion<br />
  Tree: http://permpal.com/tree/24254/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[15,x]*F[3,x]<br />
  
    F[3,x] = F[1,x]+F[23,x]+F[4,x]<br />
  
    F[4,x] = F[15,x]*F[5,x]<br />
  
    F[5,x] = F[6,x,1]<br />
  
    F[6,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[16,x,k[0]]+F[7,x,k[0]]<br />
  
    F[7,x,k[0]] = F[8,x,k[0]]<br />
  
    F[8,x,k[0]] = F[12,x,k[0]]*F[6,x,k[0]]*F[9,x,k[0]]<br />
  
    F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]<br />
  
    F[10,x,k[0]] = F[11,x,k[0]]<br />
  
    F[11,x,k[0]] = F[12,x,k[0]]*F[9,x,k[0]]<br />
  
    F[12,x,k[0]] = k[0]*x<br />
  
    F[13,x,k[0]] = F[14,x,k[0]]*F[15,x]<br />
  
    F[14,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])<br />
  
    F[15,x] = x<br />
  
    F[16,x,k[0]] = F[15,x]*F[17,x,k[0]]<br />
  
    F[17,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])<br />
  
    F[18,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[19,x,k[0]]+F[21,x,k[0]]<br />
  
    F[19,x,k[0]] = F[20,x,k[0]]<br />
  
    F[20,x,k[0]] = F[12,x,k[0]]*F[18,x,k[0]]*F[9,x,k[0]]<br />
  
    F[21,x,k[0]] = F[22,x,k[0]]<br />
  
    F[22,x,k[0]] = F[15,x]*F[5,x]*F[9,x,k[0]]<br />
  
    F[23,x] = F[15,x]*F[24,x]<br />
  
    F[24,x] = F[18,x,1]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{15}\! \left(x \right) F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = F_{15}\! \left(x \right) F_{5}\! \left(x \right)<br />
  
    F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)<br />
  
    F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{7}\! \left(x , y\right)<br />
  
    F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)<br />
  
    F_{8}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{6}\! \left(x , y\right) F_{9}\! \left(x , y\right)<br />
  
    F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)<br />
  
    F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)<br />
  
    F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{9}\! \left(x , y\right)<br />
  
    F_{12}\! \left(x , y\right) = y x<br />
  
    F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{15}\! \left(x \right)<br />
  
    F_{14}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}<br />
  
    F_{15}\! \left(x \right) = x<br />
  
    F_{16}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{17}\! \left(x , y\right)<br />
  
    F_{17}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}<br />
  
    F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y\right)<br />
  
    F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)<br />
  
    F_{20}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{9}\! \left(x , y\right)<br />
  
    F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)<br />
  
    F_{22}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)<br />
  
    F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{18}\! \left(x , 1\right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_15(x)*F_3(x))<br />
  
    Eq(F_3(x), F_1(x) + F_23(x) + F_4(x))<br />
  
    Eq(F_4(x), F_15(x)*F_5(x))<br />
  
    Eq(F_5(x), F_6(x, 1))<br />
  
    Eq(F_6(x, k_0), F_1(x) + F_13(x, k_0) + F_16(x, k_0) + F_7(x, k_0))<br />
  
    Eq(F_7(x, k_0), F_8(x, k_0))<br />
  
    Eq(F_8(x, k_0), F_12(x, k_0)*F_6(x, k_0)*F_9(x, k_0))<br />
  
    Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0))<br />
  
    Eq(F_10(x, k_0), F_11(x, k_0))<br />
  
    Eq(F_11(x, k_0), F_12(x, k_0)*F_9(x, k_0))<br />
  
    Eq(F_12(x, k_0), k_0*x)<br />
  
    Eq(F_13(x, k_0), F_14(x, k_0)*F_15(x))<br />
  
    Eq(F_14(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))<br />
  
    Eq(F_15(x), x)<br />
  
    Eq(F_16(x, k_0), F_15(x)*F_17(x, k_0))<br />
  
    Eq(F_17(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))<br />
  
    Eq(F_18(x, k_0), F_1(x) + F_16(x, k_0) + F_19(x, k_0) + F_21(x, k_0))<br />
  
    Eq(F_19(x, k_0), F_20(x, k_0))<br />
  
    Eq(F_20(x, k_0), F_12(x, k_0)*F_18(x, k_0)*F_9(x, k_0))<br />
  
    Eq(F_21(x, k_0), F_22(x, k_0))<br />
  
    Eq(F_22(x, k_0), F_15(x)*F_5(x)*F_9(x, k_0))<br />
  
    Eq(F_23(x), F_15(x)*F_24(x))<br />
  
    Eq(F_24(x), F_18(x, 1))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;place_col&#34;: true, &#34;place_row&#34;: false, &#34;strategy_class&#34;: &#34;RowAndColumnPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.rearrange_assumption&#34;, &#34;strategy_class&#34;: &#34;RearrangeAssumptionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.assumption_insertion&#34;, &#34;strategy_class&#34;: &#34;AddAssumptionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.fusion.fusion&#34;, &#34;strategy_class&#34;: &#34;FusionFactory&#34;, &#34;tracked&#34;: true}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;col_placements_tracked_fusion&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 4, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 4, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 4, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 4, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 4, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 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4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 4, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 3, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 4, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 3, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 4], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 4], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 3], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 4], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 4, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 3, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 4, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 3, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 4], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 4], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 4], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 4], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 4], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 2], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 2], [0, 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{&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, 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[[1, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 2], [0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 2], [0, 4], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 2], [0, 4], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 4, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 3, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 4, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 3, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 3], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 4], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 3], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 4, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 3, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 1, 4, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 2, 3, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: 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{&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, 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{&#34;patt&#34;: [0, 1, 3, 4, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 4, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 3, 4, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 4, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, 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2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 4, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 3, 4, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 4, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 3, 4, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 1, 4, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, 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4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 1, 4, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 3, 2, 4, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 1, 3, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 4, 2, 3, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[2, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2], [0, 3], [0, 4]], [[1, 0]], [[2, 1]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], 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&#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}}, &#34;rule_class&#34;: &#34;EquivalenceRule&#34;}]}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;rule_class&#34;: &#34;EquivalencePathRule&#34;, &#34;rules&#34;: [{&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;original_rule&#34;: {&#34;children&#34;: [{&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[2, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], 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