Details Page for 0.7172

Complete Solution is Known:

MSV File: q-0.7172.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₇(0.7172):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u | a²=1, b²⁰=b¹⁸, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, b²e=ab⁷, ce=b⁷, de=b⁹, e²=b¹⁰, b³f=ab⁹, cf=ab²f, df=b¹⁰, ef=b¹¹, f²=b¹², b⁴g=ab¹¹, cg=ab²g, dg=b¹¹, eg=b¹², fg=b¹³, g²=b¹⁴, b⁵h=ab¹³, ch=ab²h, dh=ab⁴h, eh=b¹³, fh=b¹⁴, gh=b¹⁵, h²=b¹⁶, b⁶i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=ab⁵i, fi=b¹⁵, gi=b¹⁶, hi=b¹⁷, i²=b¹⁸, b⁷j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=ab⁵j, fj=ab⁶j, gj=b¹⁷, hj=b¹⁸, ij=b¹⁹, j²=b¹⁸, b⁸k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁵k, fk=ab⁶k, gk=ab⁷k, hk=b¹⁹, ik=b¹⁸, jk=b¹⁹, k²=b¹⁸, b⁸l=b⁷k, cl=ab²l, dl=ab⁴l, el=ab⁵l, fl=ab⁶l, gl=ab⁷l, hl=ab⁷k, il=b¹⁹, jl=b¹⁸, kl=b¹⁹, l²=b¹⁸, b⁷m=b⁶l, cm=ab²m, dm=ab⁴m, em=ab⁵m, fm=ab⁶m, gm=ab⁶l, hm=ab⁷l, im=ab⁷k, jm=b¹⁹, km=b¹⁸, lm=b¹⁹, m²=b¹⁸, b⁶n=b⁵m, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=ab⁵m, gn=ab⁶m, hn=ab⁶l, in=ab⁷l, jn=ab⁷k, kn=b¹⁹, ln=b¹⁸, mn=b¹⁹, n²=b¹⁸, b⁵o=b⁴n, co=ab²o, do=ab⁴o, eo=ab⁴n, fo=ab⁵n, go=ab⁵m, ho=ab⁶m, io=ab⁶l, jo=ab⁷l, ko=ab⁷k, lo=b¹⁹, mo=b¹⁸, no=b¹⁹, o²=b¹⁸, b⁴p=b³o, cp=ab²p, dp=ab³o, ep=ab⁴o, fp=ab⁴n, gp=ab⁵n, hp=ab⁵m, ip=ab⁶m, jp=ab⁶l, kp=ab⁷l, lp=ab⁷k, mp=b¹⁹, np=b¹⁸, op=b¹⁹, p²=b¹⁸, b³q=b²p, cq=ab²q, dq=ab³p, eq=ab³o, fq=ab⁴o, gq=ab⁴n, hq=ab⁵n, iq=ab⁵m, jq=ab⁶m, kq=ab⁶l, lq=ab⁷l, mq=ab⁷k, nq=b¹⁹, oq=b¹⁸, pq=b¹⁹, q²=b¹⁸, b²r=bq, cr=abq, dr=ab²p, er=ab³p, fr=ab³o, gr=ab⁴o, hr=ab⁴n, ir=ab⁵n, jr=ab⁵m, kr=ab⁶m, lr=ab⁶l, mr=ab⁷l, nr=ab⁷k, or=b¹⁹, pr=b¹⁸, qr=b¹⁹, r²=b¹⁸, bs=r, cs=abr, ds=ab²q, es=ab²p, fs=ab³p, gs=ab³o, hs=ab⁴o, is=ab⁴n, js=ab⁵n, ks=ab⁵m, ls=ab⁶m, ms=ab⁶l, ns=ab⁷l, os=ab⁷k, ps=b¹⁹, qs=b¹⁸, rs=b¹⁹, s²=b¹⁸, bt=s, ct=ar, dt=abq, et=ab²q, ft=ab²p, gt=ab³p, ht=ab³o, it=ab⁴o, jt=ab⁴n, kt=ab⁵n, lt=ab⁵m, mt=ab⁶m, nt=ab⁶l, ot=ab⁷l, pt=ab⁷k, qt=b¹⁹, rt=b¹⁸, st=b¹⁹, t²=b¹⁸, bu=t, cu=as, du=abr, eu=abq, fu=ab²q, gu=ab²p, hu=ab³p, iu=ab³o, ju=ab⁴o, ku=ab⁴n, lu=ab⁵n, mu=ab⁵m, nu=ab⁶m, ou=ab⁶l, pu=ab⁷l, qu=ab⁷k, ru=b¹⁹, su=b¹⁸, tu=b¹⁹, u²=b¹⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, ae, abf, ag, ab²g, abh, ab³h, ai, ab²i, ab⁴i, abj, ab³j, ab⁵j, ak, ab²k, ab⁴k, ab⁶k, abl, ab³l, ab⁵l, ab⁷l, am, ab²m, ab⁴m, ab⁶m, abn, ab³n, ab⁵n, ao, ab²o, ab⁴o, abp, ab³p, aq, ab²q, abr, as, au}

Phi = 1 a b a 1 ab 1 ab b a b c ac ab ac ab³ b³ ab² b³ d b⁴ ab³ b⁴ e b⁵ ab⁴ b⁵ f b⁶ ab⁵ b⁶ g b⁷ ab⁶ b⁷ h b⁸ ab⁷ b⁸ i b⁹ ab⁸ b⁹ j b¹⁰ ab⁹ b¹⁰ k b¹¹ ab¹⁰ b¹¹ l b¹² ab¹¹ b¹² m b¹³ ab¹² b¹³ n b¹⁴ ab¹³ b¹⁴ o b¹⁵ ab¹⁴ b¹⁵ p b¹⁶ ab¹⁵ b¹⁶ q b¹⁷ ab¹⁶ b¹⁷ r b¹⁸ ab¹⁷ b¹⁸ s b¹⁹ ab¹⁸ b¹⁹ t b¹⁸ ab¹⁹ b¹⁸ u b¹⁹ ab¹⁸ b¹⁹

Monoid Structure