Details Page for 0.454

Complete Solution is Known:

MSV File: q-0.454.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₉(0.454):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t | a²=1, b³=b, c⁴=c², bd=ab, d²=b², be=b²c, ce=bc², e⁴=e², bf=b²c, cf=bc², f²=b²c², bg=ab, cdg=acd, e³fg=efg, g²=ag, bh=b²c, ch=bc², e³h=eh, efh=bc³, gh=abc, h²=fh, bi=b²c, ci=bc², dei=adefg, e³i=ei, fi=b²c², dgi=dfg, egi=aei, dhi=dfh, ehi=bc³, i²=b²c², bc²j²=bc², bcj⁴=bcj², e²j⁴=e²j², efj⁴=efj², egj⁴=egj², fgj⁴=fgj², ehj⁴=ehj², eij⁴=eij², gij⁴=gij², bj⁵=bj³, cj⁵=cj³, ej⁵=ej³, gj⁵=gj³, hj⁵=hj³, j⁶=j⁴, bk=bc, c³k=ck, ek=bc², fk=bc², gk=ak, hk=bc², ik=bc², j⁵k=j³k, k²=b²c², bl=ab, cdl=adk, del=bc, e²l=deh, efl=ab²c², cgl=acl, egl=bc, fgl=bc, ehl=ab²c², dil=dfl, eil=ab²c², gil=bc, ej⁴l=ej²l, kl=ab²c, l²=b², bm=ab, cm=cl, dm=dl, em=abc, fm=fl, gm=gl, hm=hl, im=il, km=ab²c, lm=b², m²=b², bn=bj, cgn=acn, egn=abcj, fgn=abcj, ehn=b²c²j, ein=b²c²j, gin=abcj, j⁴n=j²n, eln=abcj, mn=ln, n²=b²j², bo=ab²c, co=abc², do=bc, eo=de³fjn, go=bc, ho=ab²c², fj³o=ab²c²j, ij³o=ab²c²j, j⁵o=j³o, ko=abc², ilo=flo, j³lo=bcj³, mo=lo, no=abcj, o²=b²c², c²p=ac²ln, e³fp=efp, cgp=acp, defgp=adefp, dehp=de³fn, fhp=afhln, dip=dfp, hip=ahiln, bcj³p=bcjp, j⁴p=j²p, kp=b²cp, clp=ab²cp, dlp=b²p, flp=abcp, glp=b²p, hlp=abcp, ilp=abcp, mp=ab²p, np=b²jp, op=abcp, b²p²=p², dp²=ap², ep²=bcp², fp²=bcp², gp²=ap², hp²=bcp², ip²=bcp², cj²p²=cp², j³p²=jp², lp²=ap², p³=jp², bq=bp, cdq=cdp, e³fq=efq, gq=gp, ehq=b²c²j, fhq=afhln, iq=ip, dej²q=adegj²p, dfj²q=dfj²p, efj²q=aefgj²p, j⁴q=j²q, kq=b²cp, lq=ab²p, mq=ab²p, nq=b²jp, oq=abcp, pq=p², q²=p², b²cr=cr, c²r=ab²c², cdr=acr, e²r=ae³fjn, fr=bcr, gr=ab²r, hr=bcr, ir=bcr, j⁴r=j²r, kr=cr, lr=ab²r, mr=ab²r, nr=b²jr, or=abcr, b²pr=pr, dpr=apr, epr=bcpr, j²pr=pr, cp²r=acp², qr=pr, b²r²=r², dr²=ar², er²=bcr², j²r²=r², cpr²=acpr, r³=ar², bs=ab, cs=ab²c, e²s=ae³fjn, fs=abc, gs=b², hs=abc, is=abc, dej²s=aj⁴o, ej⁴s=ej²s, j⁵s=j³s, ks=ab²c, ls=b², ms=b², ns=ab²j, os=bc, ps=ab²p, qs=ab²p, rs=ab²r, s²=b², b²ct=ct, c²t=bc³, cdt=act, e²t=bc³, eft=bc³, cgt=act, fgt=abct, eht=bc³, fht=bc³, eit=bc³, git=abct, hit=bc³, hjt=fjt, degj³t=adej³t, cj⁴t=cj²t, dej⁴t=adegj²t, fj⁴t=fj²t, ij⁴t=fj²t, kt=ct, clt=act, elt=dft, flt=abct, glt=b²t, ilt=abct, djlt=b²jt, j⁵lt=j³lt, jmt=ab²jt, cnt=cjt, dnt=ab²jt, fnt=bcjt, gnt=ab²jt, hnt=bcjt, int=bcjt, j²nt=b²j³t, lnt=ab²jt, ot=abct, dpt=ab²pt, fpt=bcpt, gpt=ab²pt, hpt=bcpt, ipt=bcpt, cj³pt=cjpt, ej³pt=ejpt, lpt=ab²pt, qt=b²pt, b²rt=rt, drt=art, ert=bcrt, p²rt=aj²p²t, pr²t=aprt, st=ab²t, t²=b²c²>

P = {a, b², c², b²c², acd, ac³d, ae, ae², ae³, de³, adef, ag, ac²g, ae²g, de²g, aefg, defg, adh, eh, adeh, fh, ei, dej, afj, ae²fj, de²fj, ij, adij, j², b²j², c²j², acdj², ac³dj², e²j², ade²j², aefj², ae³fj², agj², ac²gj², ae²gj², de²gj², aefgj², defgj², adhj², aehj², fhj², eij², ej³, adej³, e³j³, ade³j³, afj³, dfj³, ae²fj³, de²fj³, ahj³, dhj³, ae²hj³, de²hj³, ij³, adij³, j⁴, b²j⁴, c²j⁴, adj⁴, ac²dj⁴, agj⁴, ac²gj⁴, dgj⁴, fhj⁴, adfhj⁴, hij⁴, afj⁵, dfj⁵, cj⁴k, acdj⁴k, al, ac²l, gl, dhl, afhl, dfjl, aijl, ac²j²l, gj²l, dhj²l, afhj²l, ej³l, dfj³l, aij³l, ac²j⁴l, dj⁴l, gj⁴l, adgj⁴l, afhj⁴l, dfhj⁴l, ahij⁴l, am, aj²m, aj⁴m, jn, c²jn, adjn, ac²djn, e²jn, ade²jn, efjn, adefjn, e³fjn, ade³fjn, agjn, dgjn, fhjn, adfhjn, hijn, aj³n, c²j³n, acdj³n, ac³dj³n, aej³n, ae²j³n, ae³j³n, de³j³n, adefj³n, agj³n, adhj³n, fhj³n, cjkn, acdjkn, ajln, ac²jln, djln, gjln, adgjln, afhjln, dfhjln, ahijln, aj³ln, ac²j³ln, gj³ln, dhj³ln, afhj³ln, afo, afj²o, jp, b²jp, adjp, e²jp, ade²jp, efjp, adefjp, agjp, dgjp, ae²gjp, de²gjp, aefgjp, ehjp, eijp, j³p, b²j³p, dej³p, e²j³p, de³j³p, aefj³p, agj³p, adegj³p, ae²gj³p, ade³gj³p, adhj³p, aehj³p, eij³p, ajlp, p², j²p², jq, c²jq, dejq, e²jq, de³jq, acj³q, ac³j³q, adhj³q, ar, ab²r, dr, abj²r, abjpr, abp²r, r², jpr², p²r², as, ds, bct, et, adet, ft, adft, aegt, degt, ht, it, adit, ab²j²t, ej²t, adej²t, gj²t, adgj²t, abcj³t, egj³t, aij³t, dij³t, dj⁵t, ahlt, j²lt, ejnt, ajpt, ab²jpt, abcj²pt, ap²t, abcjp²t, abcrt, cj³rt, bcr²t}

Phi = 1 1 a a b b ab c a d e f ab b b ab² g h i j k acl ab²c bj l m n ab ab b²c b²c o bc afl p q b²c³ r s t

Monoid Structure