Details Page for 0.1667

Complete Solution is Known:

MSV File: q-0.1667.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₈₃(0.1667):

Q = <a,b,c,d,e,f,g,h,i,j,k,l | a²=1, b³=b, bc=ab, c²=b², d²=1, be=bd, e²=b², cf=ab²f, f²=b², bg=ab, cg=ac, eg=ae, fg=af, g²=ag, bh=ab, ch=b², eh=ce, fh=ab²f, gh=ah, h²=b², b²i=i, ci=ai, ei=di, gi=ai, hi=ai, i²=b², b²j=j, cj=aj, ej=dj, gj=aj, hj=aj, j²=b², b²k=k, ck=ak, ek=dk, gk=ak, hk=ak, k²=b², b²l=l, cl=al, el=dl, gl=al, hl=al, l²=b²>

P = {a, b², ad, cd, adef, dg, ah}

Phi = 1 a 1 1 bd bd abd b b a c d e bd bd ab b f g h abd abd bdf ab b b b²f b²d b²d abdf bdf ab² abd ab²f b²f b²f b²d ab²d bdf b b abd abd b²f b²d ab² ab² bdf bdf bf abf ab²df b²d b²d abdf b i bf ai bdi ab²df b²df bi bi abf b²d b di abdi b²df b²f b²f ai abf abdf b b²d b²d b²df bi bi abf bdf bdf abdf afi abd abd ab²f ab² ab² di bdf bdf b²d b²f ab²f b b abdf abdf i b²d b²f b²f ab²df ab di di abd b²d ai ab² b²f bdi bdf bd i b²d b²d ab² ab² bdi afi abd abd i i abdfi bfi abdi abdi b²d ai adi adi abfi ab² bdi bdi j abd abd b b ab² abdfi b²d b²d ab²df j ab b²f ab² ab² ai b²d aj j b b abf bdj bdj b²d aj ab² ab² afi b²f b²f bdfi ab²d ab²d bfi j b abd abd abdj bj bdf ab² abf abf bdj bdj ab²df b²df b ab² i abf dfi dfi bdi abdi abdi ab² ab² b²d b²d b afi ab²df ab²df b²f b²f fj adj di afi adfi fi ab²df b²f j j aj di abdf abd abd ab² ab² afj j adi bdf adj bi b²f ab²f ab² j abdf bdf i adfi bi bi ab²df ab²df di abd b²d abf b²f bj bdi ab²df ab²df adj b²d b²d afi bj abfj abdi afj abdfi bd i i bfi bfi abdi abdi abd dj dfj abf bdij bdfj bdi b²d adj abd b b ab² ab² abdj b²d ab²df ab²df ab b fij ab² ab² ij adij abfi aj b b abf bfj abdfi abdfi adij j aj afj afj bdfi ab²d abj bfi bfi b b abd abd fij bdf bdf abdfij j adj adj adij dfj bj b abfi bdfi abi abdfij j fi bdf bdj bfi b²d b²d dfj dfj ab²df k bdj bdj abi abf abdfi di aj b fij abfj abi abfi afj j bij b fi bdj ab² k dfj adi bdf adj adj adfi bdj afij abdi abdf bdf i i bfj abi ab²df ab²df j abij abd abd bdfij b²f fi ab²df ab²df dfj adj abf abf di bfj bdi b²d b²d afj i i j ij abdi abdi abd abd bf abf adi adi aij b²f abdfi abi fj ab² dfj adi adi bfj bdj abi b²f abij ab² bdf ai abdfi abdfj abi abi b afj abf b²d b²d k bfj ak bdk bdi afj i abk abij abfij ij b b abd abd ak abdfj abj ab² bdk b²f adj abd bdij ak b abj abdk bdk bdfi abd k bdf afij bfi dk bk adij abk ab²df dfj k bdj bdj dfk adij j aj b dk bij bfj fij abfi abk j j afi abdk b²f b²f adfk bk adi j abf abf bfj ak dfij ab² ab² abdk i adj b²f adij ab²df ab²df bfi bfi bfj abdk abdfk fi fi bdi ik bdk abf abf bk di abdfj afij afij ik aik k j adfk abdi abfk bfj b²f dik bij dfj j fk fk bfj b²f afi bk abdk bfij bfk adfi adij abi afij bfi ik bdk bdf afk bfj abdfj bdfk ab²df abj afj abij abd b²d ak abdfj jk bdi bfk ik abd abk k ab² ab² aik bfk adfi afk i k ij ij ab²df bfk abd afj b b abik afk bfj bdi abd abd abfij ab² bdjk dk b²d b²d bfj bk abdjk dfj abfi bdj abdfi abdfi bfj aj aj dfj dk bjk adfk ij ij abk bdk dfj afj afj abdj bfj ab² abk ik b adj b²f abdfk ak abdik bdf abfi ik adj adj adk abik abj abj afk bf bf abd k k abdfik abdi fij dfik abdfij adfk dfk dk ab²df ab²df bdj bdik bdk adfk j j abdfik afj b²f b²f abfi adik abk j adj afk ab² abdik afij afij abdk bdjk dj dfi bfik bfik bdfk abdfk bdf j abd afk abdik ak ab²df abj abj di bdfij abdfij abdjk dfk ab²df bdi bdi dfj bjk bjk abk bfik ab² ab²df bfk b abf afik bjk j bdfj ab²df fjk abd bfk afj dfk afi abdjk abdjk abi ajk k afj ai ab² adk dk dfik bdfi bk adik ik fi bdij abik abdik ij aij aj dfj bfk abdjk adfi k adij abdfj afik b aik abd afj k adfk bdik abdfj dfik adj adj dfj bdfjk bj dfij adij fjk abdfij j ijk adfk abjk bj afk b²d dj abdfk afik bjk ijk ijk abj dfik abdfi adj adfjk b b dk fk bdfijk bdijk bdfk j bdf bdf afk b²f b²f bi dfk abk afik di abd adfi afj b²d b²d bdf bdf abfij adj adj bjk abj b²df adjk ik j bdf dijk bfj bdik ab²df ab²df bdk abk bdfjk dfi bfij abdfj abdfj bdi djk ajk abk bdf bdf abfij abfij b²d b²d dfj dfij fik bdik ijk abdi bdfik b²f adfjk afj b b bjk abdjk abdfj b²d b²f bdfijk bdfijk afj bdf afk bik b²d b²d abfi ab²df bfi l bdjk abdjk ak aij abdfk ajk dfj dfik abij abdfjk b²d abijk abdfj abdi b afj afj bdfjk l bdik abdfj bdi abdi dfik adik abij ak ak afk abdfj ij ij abdfij fj dfj dfj abik abfi bfj bfj l adik bdij fi adk bdj dfij abdl bfij j dfj dfj abik b²f b²f ij ij adj abdfik fi abdjk afj dfij dfk adik abfijk j adj abfjk afj al al abdi bdl afjk abfij adj dfi adk al bdf bdf abdfik bdl ai bl bdfjk dfij abj abj djk dfik adj adfi bfik fl abdi bdj bdj abd abk bdijk abdl afl ab²df bfk abdj afj bk l j j ijk bdj b²f b²f dfj b dfik bfjk abik bdik bdj bdj abdi bdfijk dfj afk dfl b²d l fl bl abfi adfj abij al bdfjk abdfj abdfj fl afij abdk abdjk dfik adijk bdfjk afl abdl abdl ik bfk adfi ajk abfl abfl adij adij dfij dfij afj afj adl aijk abdfj abdfj l bdfi abk fi fi adfijk abdfik abdfj abdfj il dfjk bdfijk bdij abfl abik abik bdfi abdfi ajk bfijk dfj bdij bdij ijk ij adij afik j dfj afj adfi adijk l fl abdfj bdijk abfk dfj abdfl abdfl dfl abdik abdfj abfl dfik dj adik bdfjk abjk abjk afij abdfj abdfik abdijk abdijk abij k abj abj abik ij ij adj fik ail fl il dil abdil bdfijk adj adj ail bfij adk adil dfij l bdfil bdfil bil b²f k k dfij dfij bk abdfijk adi fi adk b²f ij adfij afij afik bfl abdfij bdfij adfl bjk dfij abdfk bdl abfijk afik abdfij abdfij k k b²d afij djk adl abij bfl bfl adfijk afl afij bdfl bfijk bfijk adl adl bfij abik abj bdj abdfl dfj bfl jl abdjk bjk ij ij adfjk adik abdil abfl bfij abik abdfik abdfi abdfi afij abfijk bdij abdjl afk afk bfj bfj abk djk bdij fi abdfjl adfijk fijk bdijk afik abdl adfil afj afj bjk dfk fl bfj adij ik ik afj ajl ajl il abfjl abdfj fjk abij abfl bij afil abjk abdjk dij ij ajk abl bil il ijk adij ajl ajl ij abk bil abil abil aijk abdj dil adfjk adfjk dik bfij bfij abik dfij al bdfil bdijk afik bil afil bdfjk abdil dfk dijk abk bfij il abl bdjl bdfjk dfij afik fij bdfijk djk abdfij abdfij adfl k adjl adjl adjk abijk fjk bdfij j abdil k bdj adjl bdk adfik abfijk bdfij fijk abdfik adfijk abdi dfij ajk jl fi bfij fijk bdfik adik adik dfij abijl bfl ab² ab² abdfik jl abdil ijl abfijk ai bfij abf bfjk afil jl jl bdl bdfijk dil bdij abdjk fijk dijk adl dij b bfij bdjl bdjl ij bdijl afl adij djk abdfk abl l bfil adfk abik abik fijl bdf bdf ajl b²f bdik abfjl adfl dfjl ik ik abf abij dfk aijk bdijl ajl bfk abl bdkl bdjl dfj abfjk adk afijl abk abk dik abdkl j bdij fk abdi fijk abdil abkl bfij bfij afjl ajl dijk bjk abdijl adfjk adij fjk afj aijk abdfij b²d b²d bdfkl adfik abdjk abjl abdil afj bdfjk afij akl adij fjk dfl abl bdil k bdfjk l l fjk dil dil abdfij k bdfjk afij ik abk abdfj fkl akl bfik bfik bdfkl abdkl aik ajk bdf bdf bdl kl adk bl abij abdfjl abk afik adfil adfil abik bdik abdil bdfkl ajk bfl afi adj bfij bjk bjk afij bdl abfl bdf fjk bfil abfkl abfkl ikl adfil djk bfk bdfjl ij j abdik fl fl bijk afij abfil bfijl dkl bdik bjk afl ik afij abdfl b abdfij il bdfil abdjk abijl adfjl abij adikl aijl afjl afk abdjk bdijl abl abdfk abdfk abfl adl abfjk abik abik bkl dfij bikl ai bdfkl kl bdik bdik dil abikl abdijk bil b akl bdfl bdijl bdfjl ijl bdfkl adij bdfijk bdikl adfil adfil dfk bfi b²d adij adij abdil dfj bdj bdj j bfjl bdk abdfj adkl adfjl bdfjk b²f b²f adfijk adfik bfj abdkl adfijl dijk bdik bdfkl bdfjk adijl adfikl abk ajk abf abf afk adk abdi abfkl jkl abk adfjk abij abdfik adk adk adfikl ikl afik adjl bdk jl bdfik bdfjk bdfjk adij bfl djkl dfkl dfjl abdjkl afl bdfkl bdfil b²f bdk adfi akl afk afijk bjk dfikl abk abk dfik abf bdf adkl j bdij bil ik bfk adfi afil fkl bdik abfjk abfjk ik adfikl jkl bfijk dkl bjk abdjk abdi abdi bdk abdfk adik fjkl dl bik abdikl bdjkl fijl fijl ajkl adfjk adfjkl afk adk adfijk adjkl abfkl ai ai ik abik abik abdfij bdik bfjl abfijk dfj abd dfjl b bdjl b²f j adfjk fjk bdfijk bl bdfikl bdjkl bdik adikl adij di bdf bdj abfijk bdfjk bdik b²f bfjl dfik bijk abk abij abij dfk abik abdijkl bkl bijk fikl bdj ijkl abijl ijl bdfjk adl abjl afik jk abf ail abdjk abik dil dil bk ij abfijk abf abdfik aijk bdij bfik ajk abdijk bdk fjl bdfikl k bdij bdik bfil abdijk bdk dfik adfjkl dfjl bdf bdjl fjl bdfijl bdk j fijkl dfl k dfj dfj bdfil ab²df ab²df jl ij ij k abdfik akl bdfkl bfk afik ijl fijk abfkl dk abfjk abdfkl ajk ajk ijkl abdfj bdikl afl abfjk adfl ab²df adij abk adfjk abd abd abik afl abdkl dfikl abfijk bdij abdfil adfijk bjk abfjkl bfkl afl bfk adik bdfijk ij ij k k bfjl aijkl djk djk abijkl bdjkl bfj

Monoid Structure