Details Page for 0.1163

Complete Solution is Known:

MSV File: q-0.1163.msv

Growth Pattern:

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Details for Q₁₃₉₉(0.1163):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v | a²=1, b⁴=b², b²c=ab², c²=b², d²=b², be=b³d, ce=ab²d, de=b², e²=b², bf=b³d, ef=b², f²=b², b²g=b³d, bcg=ab²d, bdg=b², cdg=ab³, eg=dg, cfg=ab³, dfg=b³d, bg²=dg, dg²=bg, fg³=fg, g⁴=g², bh=b²d, ch=ab³d, dh=b³, fh=eh, gh=b², h²=b², bi=ab², ci=b³, ei=ab³d, fi=ab³d, gi=abg, hi=ab²d, i²=b², bj=ab², cj=b³, dj=di, ej=ab³d, fj=ab³d, gj=afg², hj=ab²d, ij=b², j²=b², bk=b², ck=ab³, dk=b³d, ek=b³d, fk=b³d, gk=fg², hk=b²d, ik=ab², jk=ab², k²=b², bl=cg², cl=b³, dl=cg³, el=cg³, fg²l=fl, g³l=gl, hl=ab²d, il=acg², jl=afgl, kl=fgl, l²=b², bm=b³d, cm=ab²d, dm=b², em=b², fm=b², gm=b³, hm=eh, im=ab³d, jm=ab³d, km=b³d, lm=ab³d, m²=b², bn=b³d, cn=ab²d, dn=b², en=b², fn=b², g²n=n, hn=b³, in=ab³d, jn=ab³d, kn=b³d, ln=cg³, mn=b², n²=b², bo=cg², co=b³, do=cg³, fgo=fgl, g³o=go, eho=cdf, io=acg², jo=afgl, lo=b², no=ab³d, o²=b², b²p=b³d, cp=ab³d, bdp=acdf, ep=b³, fp=b³, gp=acdf, hp=b², ip=abp, jp=abp, kp=b²d, lp=ab²d, mp=b³, np=b³, op=ab²d, p²=b², bq=b³d, cq=cf, dq=df, eq=b², fq=b², gq=b³, hq=b³, iq=ab³d, jq=ab³d, kq=b³d, lq=ab³d, mq=b², nq=b², oq=ab³d, pq=b³, q²=b², b²r=ab³d, bcr=acf, bdr=adf, er=ab³, fr=ab³, gr=adf, hr=ab², ir=b²d, jr=b²d, kr=ab²d, lr=b²d, mr=ab³, nr=ab³, or=b²d, pr=ab², qr=ab³, r²=b², b³s=bs, bcs=abs, es=b²ds, fs=b²ds, gs=bds, hs=bds, is=abs, js=abs, ks=bs, ls=abs, ms=b²ds, ns=b²ds, os=abs, ps=bds, qs=b²ds, rs=abds, s²=b², b²t=t, ct=at, et=dt, ft=dt, gt=bdt, ht=bdt, it=abt, jt=abt, kt=bt, lt=abt, mt=dt, nt=dt, ot=abt, pt=bdt, qt=dt, rt=abdt, t²=b², b²u=u, cu=au, eu=du, fu=du, gu=bdu, hu=bdu, iu=abu, ju=abu, ku=bu, lu=abu, mu=du, nu=du, ou=abu, pu=bdu, qu=du, ru=abdu, u²=b², b²v=v, cv=av, ev=dv, fv=dv, gv=bdv, hv=bdv, iv=abv, jv=abv, kv=bv, lv=abv, mv=dv, nv=dv, ov=abv, pv=bdv, qv=dv, rv=abdv, v²=b²>

P = {a, b², af, adf, g, acg, ag², g³, acg³, al, ao, eo, fo, ako, mo, abp, aq, ds, acds}

Phi = 1 a a 1 b b b ab 1 a b² c ab b b d e f b² g h i b abc e ab² b² ab² b² j k b³ b³ fg² ab² cg² b³d b³d b³d l m n b²d cdf ab² b³d b³d ab³ b³ o b² ab² cdf cg² ab³ p ab³ b²d b²d q cdf r b³d ab³ ab³ s b²d fgl ko ab² acg² b³ ab³ ab³ b²d b²d ko cg² b³d b³d b³d ab²d b²d b²d b²d ab² ab³d b³d b³d ab³ ab³ ab³ ab² ab² ab² b³d ab³d b³d ab³ b²d b²d ab²d b³d ab³d b³d ab³d b²s b²d b²d ab²d bs ab² b² ab³d b²s b²s b²d b²d ab²d bs b³d b³d b³d ab²d b²d b²d b²d bs ab³d b³d b³d b²s b²s b²d b²d ab³ bs b³d ab³d ab² b²s b²d b²d ab²d b³d b³d b³d ab³d ab² b²d b²d ab²d ab³ ab³ b³d ab² ab² ab² b²d b²d ab³ ab³ b³d b³d b³d ab²d b²d b²d b²d bs ab³ b³d b³d ab² ab² b²d b³ ab³ bs b³d ab²s ab² b²d b²d b²d ab²d b³d b³d b³d ab² ab² b²d b²d ab³ ab³ ab³ b²s ab² b² ab² b²d b³ b³ ab³ b³d b³d ab² b²ds b²d b²d b³ b³ ab³ b³d b² ab² b² ab³ b³ ab³ b³ b²ds ab² ab² b²s bds b²d ab³ bs b²ds abs ab² ab² b²s bds b³ ab³ ab³ b² ab² ab² ab² b²s b³ ab³ ab³ b²ds abs b³d ab² b³d bds b³ t ab³ b²ds b² ab² b²s ab³ b³ ab³ t b²d ab² ab² bds b³d b³d ab³ b²d b²d b²d ab² ab² b³d b³ ab³ ab³ ab³ b² ab² ab² ab² b³d b³d ab³ ab³ b²d b²ds ab² ab³d b³d bds ab³ t b²d b²ds at ab² t ab³ ab²s ab³ b²d b²d ab² ab² b³d b³d b³d abds b²d b²d abs bs ab² b³d b³d b²s ab³ ab³ bs bs ab² ab² b³d b³d ab³ ab³ ab²d b²d abs ab³d ab³d b³d ab²s b²s ab²d ab²d abs ab² ab³d ab²s ab²s ab³ ab²d ab²d ab²d bs b³d ab³d ab³d b²s b²d ab²d ab²d bs abs ab³d t b²s b²s ab³ abt bs bs b³d ab³d at b²s b²d ab²d ab²d b³d ab³d ab³d ab³d ab²s b²s ab²d ab²d abs ab³ ab³d ab² ab²s ab² b²s bt abs ab³ b³d ab³d ab³d ab²d ab²d ab²d bt bs abs b²ds ab²ds ab²s b²s at b³ ab³ bs abs at t b²s b²d abds ab²d b³d b³d ab²ds at t b²d b²d abs bt ab³ bs ab²s ab²s ab² b²d bt abt ab³ b³d b³d t ab²d bds b²d ab³ abt ab³ b³d b³d t t at b³ bt bt b²ds ab²ds t b²s bds bds abds b³d b³d b²ds at t bds bds abds abt bs bs ab² at t b²s bds abds dt b²ds b²ds b²ds bdt bds bds abds dt ab³ b²ds b² t t bds bds st bt b²ds b²ds bst bdt bds bds bds dt b²d b²d at t bdt bds b³ abt st b²ds ab² at t bds b³d ab²s adt b²ds b²ds b²d abdt b³d bds bds dt bt b²ds ab² bst bs bds b³ b²s bt b²ds b²ds bst bs bds abds ab²s dt b²ds ab²ds abs abdt bs abds b²s b²s ab³ bt abs bs bs bdt st b²s b²s abt adt ab²d abdt bds abdt b²s b²s adt ab²ds b²d bs bs ab³ b²s b²s t bt abt bs bs bdt dst b²s b²s dt bt bs bs bs t b²s b²s b²s bt abs bs bs at st b²s ab²s ast ab²d bs abs abdt at b²s b²s ab²s ab²d bs bs ab³ t t ab² ab²s bt ab²d bs bs dst ast b²s b²s bdst bt bs ab³d bs t ab²s b²s b²s bt abs bs bs at t b²s ab²s ast abt bs b³d ab²ds at b²s b²s ab²s abt abs bs bs at t b²s b²s bt abs bs b³d dst u at b²s bds abds abt adst bs u at u ab² bs abs abt b²ds adst t b²s abds abds abds bt ab²ds ab²ds at bdt bdst abdst abds abdst abt bs ab²s at at b²s abds abds bt b²ds b²ds b²ds ab²d b²d bds abds abt dt bs b²ds at bdt abds ast abt abt b²ds b²ds b²ds at bds bds bds bt ab²ds b²ds b²d bst bdt bds bds ast bt bs ab²ds bst t bds bds abds bt b²ds b²ds b²ds b²d bds bds abds abt adt b²ds b²ds bst bst bds bds st abt ast b²ds abs bdt bds bds bds dt ab²ds b²ds b²ds abst at bds bds st b²s b²ds abs bs abst abdt bds b²s ast dt au ab²ds bdt bds bu ab²s b²s adt ab²ds u bs bst t b²s b²s bt dt abst bs bs t bdt abds adt u dt bs bs bs abdt b²s ab²s ab²s bt abs bs abs t st b²s b²s adt bdst bs bdt bs dst b²s b²s ab²s dt abs bs bs ab³ b²s ab²s b²s bt abst bs bs dst dst ab²s b²s b³d bt bs bs bs bdt b²s ab²s b²s b² bt bs bs ab³ t ab²s b²s bdst bdst dt bs abst at b²s b²s ab²s adt bs bs bs t b²s b²s ab²s bt ab² bs bs dst abdt ab²s b²s bds abds u abs bs ab²ds bu u b²s bt du abs bs ab³ at du b²s abds abds bt ab²ds b²ds ab²ds dst bdst bds abds u st bs ab²ds bdt bst au abds ab² dt abdu adst b²ds bdt bds b³d ab³d bt bu bs ab²ds su u au bds abds abdu b²ds b²ds dst t bds abds st bt ab²ds b²ds ab²ds adst bst abdst bds ast st bu ab²ds ab³ at abds abds abds bt ab²ds ab²ds b²d bdt bdt abdt bds st dt ab²ds b²ds bst abst abdt abdu st st adt ab²ds b²ds at abdt abds bds b³d ab²ds b²ds ab²ds abdt bst abds abds ast ab² ab²ds b²ds bs t abds su ast st b²ds absu ab²ds abdt abdu bds absu ast ast adu ab²ds bst bst at b²s b²s b² ast absu abs abst abdu dsu abds b²s b³d absu ab²ds bs bs abdu au st b²s bt su ab³ b³ at dsu ab²s ab²s bt adu bst adst bs bu bu b²s ab² bt u bs asu ab³ b²s b²s ab²s au bt bst bs dst adst abdu b²s abt bdst absu asu bs t dsu tu ab²s bt bdsu abs bs b²d absu bu ab²s bdst bdst su bs dst dst dst bsu b²s bdst atu u asu ab³ dtu b²s tu bdst btu bdsu bs ab²d dst tu asu ab³d b³d adt adsu dst abdt abdt ab²s au bt bdst abs adst dst ab²ds atu adu b³d ab³d dt abs b²ds ab²ds dst du abdst bds abds su bu ab²d abdt u u bdst abds btu asu ab²ds b²d b²ds u bdst ab³d abtu bu dst b²d bdt u au b³d abds abdu asu asu ab²ds u bds bdst bds b³d bu dst b²d ab²ds bdst abdst abdst btu bu bu ab²ds bdt abst atu bds abds adt bu adst b²ds abst bdt abdst abds abtu bu ab²ds adst bdt abst absu btu ab² st abt tu b²ds bst bst abdu bds adt bu abu adu bst bdt bdtu abu ab²s bu atu abdsu bst bst absu dsu ast bt abt atu dsu b²d bst astu abtu st asu su astu abst bs abtu dsu ab² ab² ast absu bst bs abst dsu abdu b²s dtu btu stu bst bs bdtu abu ast st st dtu bst b³ bst dsu ast ab² abt adu du ab³ dst abtu bdu ast b²s atu u bst b³ abst dsu st b² b²s bdsu bst bs adst abdu bdu b²d abdst abdst bdsu bst bst btu dsu ast tu b²s adu bst abst abs dsu dstu tu ab³d bdst du bstu dst dst abdu u ast abdst bdsu bdsu btu abs abdu bdu ab²s b²s abdst bdsu abtu b²d bdu abdstu u tu bdst bdsu asu dst dst dsu ab²ds absu b²s adu bdtu bs abs adst dstu atu ab³d abds stu bu b²d b²d abdt adsu abdst ab³d bdst btu asu ab²d ab²ds u atu bdst bdst abstu bu adst ab²ds v u u bdst abds abds dst abdu dtu atu u bdst abds bu adst ab² dtu u abt abdst adt bds v b²d ab²d ab²ds abv abdst bdst abds abtu stu ab² bst abst u ab³ st ast bu adst dst adtu bdst abdst bdst bds abstu dst adst bst atu u bdtu st ast bu adtu dst bt abst abdtu abdst bds v abu abdt ab²ds bst abdst dt st v bu adstu bst abst au dt bds ast adstu dtu dtu b²ds bv u absu abdu asu v bdt bst bdstu u bv ast st ab²s bu bdt bst bst abs abdtu dt dtu bdt bdt bdt bdstu bv dt st v b²s asu b³ ab³ bs bdtu abu st st dtu du abst u abdtu absu b²d v st bdt bst abdstu bs bs ab² b² ab²s dtu bst bst abs absu abdu st abdst abdt v bst abtu dt adt st ast b²s v abst abst bs bv bv bt st du adu v dst adst bv abdu tu abdt v at abtu abst bs bt ast abt ab²s bdv t bdtu adst bdu bv abdst abds du v abtu dt bdu adstu ast atu du abds at t bdu adsu bv abt abds bds v t adst ab²ds b²ds abt abdst abstu bds at btu adst bt abt adv abdst bdsu t t ab²ds adsu b²ds abt adu v abds av sv ab²ds u bt st abdv t t b² adstu adsu bt abdst abstu v t b²d dst b²ds b²ds bt v abdst bdsu stu ab²d dstu bt bt b³ ast at at v asv bv bt bdst abdst btu abds t abdt bst abt u b³ btu b²s ab²s at bst bt bt absu adv bdsu v t bdt ab²ds bv bt dt atu ab²s b²s t dtu bt bs ab³ abdtu at t b²s bdt abst bv abt dt absv v v bdt bdt abst abstu absu adt ast b²s ab²s bst u adv adt dt dt adstu bdt bdt bdt b²ds adt adt dt b²s b²s bdt bdt bst abs dt bsv abdtu v abdt abst adst bv dt dt b²d asu astu bdt bdt absu bv dt adt tu b²s abdt bdt ab³d absu bv dt adt ab²d bds bdt b³d bstu bdtu b²ds dt asu asv bdt at abdstu dv dt abt bt abdv abds bdt abdstu asv adt b²ds dt adstu dsu bdt abdt v absu dt bt b²d bdv ab²s abdt abtu sv abdtu ab²ds adt bv abdt abds bds v dt sv bt bt absv abdstu abds t t adv adsu bt abt abds bds sv tv ab²ds b²ds adt abt tv v t t ab² b²ds bt b³ bt abdv abdstu t t ab²ds ab²ds bt bt v bds bds t bv dstu bt bt absv abstu t t b² adv bv abt abt abdv bds abdstu t asv stu bs bdst atu absv t t ab² dstu abs bt ab³ tv abdv t t asv b²ds bt bt bv abds t t ab² sv bt bt bstu abdstu b²s ab² t asv bv bt abs abdsu bsv v t bdt bv bt abt adt absu t b²s t sv dsu bs dt bdtu bsv ab²s t sv bv bv abt dt dt bsv b²s bdt bv asv bs bt dsv dsv abdv t abdt bdsv abt bt dt absv dsv bdt bdt ab³d b³d dt adt dt av ab²s bdt bdt ab³d absu dt dt adv abdv abds bdt bdsv bstu ab²ds dt ab²d v stu bdt bdt absu abs dt dt ab²s b²s bdt bdt bdsv bstu dt dt b²d bsv bds abdt bdt bstu adt adt dt ab²s b²s bdt bdt bs dv dt adt asu stu bdt abds tv asv ab²ds dt ab²d bsv abdv abds bdt absu bs dt bt adstu abdv bdt bdt asv bdsv adt adt abt dsu atv abdt bdt btu absu dt ab²ds adstu v bdtv t ab² adv adv adt abt absv absv abds abds t adv adt dt ab³ absv bdt bdstu adtu bv adstu adv ab³ ab³ abdv t t ab² adv ab²ds dstu ab³ v abdstu bdt bdsu asv tu adstu bt absv abdv at at ab² dsu adv abt b²d abdv abds t ab² bv ab²ds btv v ab²d btu t atv adv asv u bt ab³ v b²s ab²s ab² u dstu bt bt b²d bsv atv t b³d adstu dstu bt bt abdtu bdstu ab²s adv sv atu abt btv ab²d abdstu t t ab³d asv asv bt abstu absu absv tv at asu abv bt ab³ abdtu adv t stu ab² sv abdsv bt b²d b²d astu t abdu bv bv bt abtv bdv v adsv t b³d asv abt abdu bsu dsv astu v b³d b³d ab³d bstu dst b³ av stu abdt asu ab³d bstu bstu b²d b³ adsv atv b³d sv bstu abstu b²d ab²d astu stu stu abdt sv abstu bdtu btv dsv abdv bdt bdtv bdsv bstu btv btv v bsv stu b³d abdt bdsv bstu dt dt v stu abdt abdt ab² absu abdtu adt b³ astu bdv abdt abdt bstu abtv dt u stu astu tv bdt bv asv adtv adt ab²d dstu abdtv bdt absu bdsv adtv btv b³ absv v abdt bdt bsu abstu dstu dt v dsv bdt abdt ab² at bdsv adt abt abdv dsv abdstu abdt at sv dt adstu bsv abdv bdt bdt bdstu adv adstu btv b³ b³ bdv abtu bdstu ab² adv adstu bt adstv ab³ abdv bdt ab³d adv dstu bt asu bds dsv tv bdstu b³d sv dstu dstu abdv abdu abdstu abdstu adu dsu stv dstu btv abdv bstv t tv b³d tu adstu ab³ bdv abdsu dtu st dv asv bdstv tu abdv ab²d bsv tv tv ab²ds abdsv btv abtv bt bdsu abtu bdtv adv ab² dstu adstu abdu ab²d abdstu tv tv bv adstu asv bt v b²d bsv tv b³d adv abdsv ab³ ab³ ab²d abdv at tv abdst adstu bdtu btv abstu bsv absv tv ab² bv asv bstu bt ab²d b²d bdtv t abdsv dstu btv abstu dst bsv adu tv b³d sv abv abstu b²d ab³ abstv stu tv bdst asv astv abstu ab³ ab³ adsv tv b³d bv abtv bdstv abstu v b²d dtu astu stv abdsv bstu bstu b²s ab³ stu tv b³d ab² bstu abtv b²d abdv adsv bdtv atv abdstv bdst abstu bstu av ab³ stu astu b³d adv bstu abtv atu b³ abst tv tv bdu bu btv adt v stu astu atv bv ab² ast abtv u b³ stu adstv atv ab² astv adtv btv av v stu atv bv abv bstu tu adtv abuv stu bdtv abdstu ab² adv bdsv dtv ab³ dsv adstv atv abdu abdstu abv v adstu au abdv bu bdstu b² ast asv adstu ab³ bst uv abdtv bdstu st bdsv dtv adstu abst bv tv ab²ds auv b³d du btv b³ bdv absv abstv abdstu dv bdsv dstu dstu adstv abdv bdstu abdstu ab² b³d dtv adstu bst abdv bsv bstv auv adv sv abtv abdv ab³ abstv bdstu abdstu dv b³d dstu abtv abtv bst bdstu atv tv b³d dsu dstu abdv abuv abdu abdstu adv ab² dv btv adstu ab³ dsv bstv tv au u dstu stv abds b²d ab²d dtu bstv bduv au dstu abdv bdv abdu abdstu abstv dtu adsu dstu astv stv ab³ bdstu tv adstv abuv b³d astv bstu bstu dst adstv au b²ds adstu abdtu abdtu abdtu buv bstv bstv adu uv asv auv btv abstu ab³ suv tv astu b³d bdst btv dtv adst b²d tv atv abuv bduv bdtu b²s auv ab²d adstv stu suv bduv b³d bdtu bds duv adtu u astu bdtv abdtu abdtu abdv av b²d u b²ds bduv uv abu bstu bstu b²d u tv stu bduv absuv abdtu abtv dtv abstv astu bs abdtv dsuv bdtu bstu bsuv atu absv astu tv bduv b² ast astv u dsv stu astu auv ast adv dtv atu adu dstv ab³ abdtv auv abdt stv adtv dtv stu bst b²ds abtu absuv adv adtv stv abdsuv ab³ dstv tv bu ast astv btv au adsu astu bdtv bs abdsu stv adtv b²s duv ab³ abstv bs adsuv uv ast abds abds abdv bstv stu ab²ds auv sv atu abuv dsu abuv stu tv adsuv dsuv abdstv btv abdsuv adstv suv btu bduv ast bduv tu abuv buv ab³ dstv b²ds b²ds bduv abduv b²s duv abuv ab³ bs abs bsuv bsuv adstu abuv abuv abdv btu adt auv bdstv atu atu suv aduv abdu abstv ab² auv bdsv b²s abds abuv bdv tv bs ab² ab² adstu dstu abdtu suv bstv ab²ds tuv bsuv absuv bdst btv ab³ dstv adstv bstv tuv ab² abduv b²s ab²s absv ab²d abstv abdtv asu astv atuv b²s suv dsv dst bs adv su astv ab²s dtuv bdsuv abdstu bstv adtu bduv astv bdstv abstu buv ab³ duv abs abduv b³d stv b²s stuv bdsuv bt atv du bduv bduv stv b²s bdsuv abuv abdsuv ab²ds b²ds stv adsuv abds aduv duv bt bt abs abdsu auv tuv bdtu abdsuv abuv dtu bs adsuv auv stv bdtu bds abdsuv abdsuv ab²ds bduv ab³d uv stv abtv abuv adtu bt ab²ds bdsu auv abu astv bds adsu au dtu b²ds ab²ds bstu asv abds bds suv atv abt dsuv auv t bdstv t abdsuv ab³ adstv ab²ds ab²ds asv at abds abtuv buv atv b²ds adtuv astv stv b²s bds abuv abt dstv ab²ds abdsu bsuv bdstv bdt abds tv tv b²ds ab³d absuv at abds au suv duv bstv abdsu tuv t st abds adtuv buv adstv b²ds bs auv abdt astv bdt absu adstv bstv bdsu abduv bsuv stv b²s abuv abuv bstv bs abtuv uv bdtuv b²s abdt suv absv abtu abs absuv auv abdt atu duv dtuv duv abs bsuv bsuv asu astv b²s stuv abtu adt adtuv tuv atu bdt ab²s bdt absu adt asu bs bduv bduv abdt b²s b²s buv adt bs ab² uv bdt bdt asuv aduv dt abs bs atu bdt abdtuv b²s absu abtu bt abs asu auv abdt b²s b²s dstv adstv abs abs tu abdstv abdstv ab²s abtu btu dt bs adu bdstv abdt ab²s asuv bdtu dstv bs adtu auv abdt bdstuv b²s abuv adt bstv bs adu auv bv t b²s duv dsu bs bt bduv abdt abdt astuv buv asuv abdtuv ab²ds dstuv uv abdstuv abds abdsuv buv stuv dtu atu abdstuv astv stv

Monoid Structure