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 Q₉₉(0.7172):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x | a²=1, b²³=b²¹, 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=b²⁰, b⁸k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁵k, fk=ab⁶k, gk=ab⁷k, hk=b¹⁹, ik=b²⁰, jk=b²¹, k²=b²², b⁹l=ab²¹, cl=ab²l, dl=ab⁴l, el=ab⁵l, fl=ab⁶l, gl=ab⁷l, hl=ab⁸l, il=b²¹, jl=b²², kl=b²¹, l²=b²², b¹⁰m=ab²¹, cm=ab²m, dm=ab⁴m, em=ab⁵m, fm=ab⁶m, gm=ab⁷m, hm=ab⁸m, im=ab⁹m, jm=b²¹, km=b²², lm=b²¹, m²=b²², b⁹n=b⁸m, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=ab⁶n, gn=ab⁷n, hn=ab⁸n, in=ab⁸m, jn=ab⁹m, kn=b²¹, ln=b²², mn=b²¹, n²=b²², b⁸o=b⁷n, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=ab⁶o, go=ab⁷o, ho=ab⁷n, io=ab⁸n, jo=ab⁸m, ko=ab⁹m, lo=b²¹, mo=b²², no=b²¹, o²=b²², b⁷p=b⁶o, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=ab⁶p, gp=ab⁶o, hp=ab⁷o, ip=ab⁷n, jp=ab⁸n, kp=ab⁸m, lp=ab⁹m, mp=b²¹, np=b²², op=b²¹, p²=b²², b⁶q=b⁵p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=ab⁵p, gq=ab⁶p, hq=ab⁶o, iq=ab⁷o, jq=ab⁷n, kq=ab⁸n, lq=ab⁸m, mq=ab⁹m, nq=b²¹, oq=b²², pq=b²¹, q²=b²², b⁵r=b⁴q, cr=ab²r, dr=ab⁴r, er=ab⁴q, fr=ab⁵q, gr=ab⁵p, hr=ab⁶p, ir=ab⁶o, jr=ab⁷o, kr=ab⁷n, lr=ab⁸n, mr=ab⁸m, nr=ab⁹m, or=b²¹, pr=b²², qr=b²¹, r²=b²², b⁴s=b³r, cs=ab²s, ds=ab³r, es=ab⁴r, fs=ab⁴q, gs=ab⁵q, hs=ab⁵p, is=ab⁶p, js=ab⁶o, ks=ab⁷o, ls=ab⁷n, ms=ab⁸n, ns=ab⁸m, os=ab⁹m, ps=b²¹, qs=b²², rs=b²¹, s²=b²², b³t=b²s, ct=ab²t, dt=ab³s, et=ab³r, ft=ab⁴r, gt=ab⁴q, ht=ab⁵q, it=ab⁵p, jt=ab⁶p, kt=ab⁶o, lt=ab⁷o, mt=ab⁷n, nt=ab⁸n, ot=ab⁸m, pt=ab⁹m, qt=b²¹, rt=b²², st=b²¹, t²=b²², b²u=bt, cu=abt, du=ab²s, eu=ab³s, fu=ab³r, gu=ab⁴r, hu=ab⁴q, iu=ab⁵q, ju=ab⁵p, ku=ab⁶p, lu=ab⁶o, mu=ab⁷o, nu=ab⁷n, ou=ab⁸n, pu=ab⁸m, qu=ab⁹m, ru=b²¹, su=b²², tu=b²¹, u²=b²², bv=u, cv=abu, dv=ab²t, ev=ab²s, fv=ab³s, gv=ab³r, hv=ab⁴r, iv=ab⁴q, jv=ab⁵q, kv=ab⁵p, lv=ab⁶p, mv=ab⁶o, nv=ab⁷o, ov=ab⁷n, pv=ab⁸n, qv=ab⁸m, rv=ab⁹m, sv=b²¹, tv=b²², uv=b²¹, v²=b²², bw=v, cw=au, dw=abt, ew=ab²t, fw=ab²s, gw=ab³s, hw=ab³r, iw=ab⁴r, jw=ab⁴q, kw=ab⁵q, lw=ab⁵p, mw=ab⁶p, nw=ab⁶o, ow=ab⁷o, pw=ab⁷n, qw=ab⁸n, rw=ab⁸m, sw=ab⁹m, tw=b²¹, uw=b²², vw=b²¹, w²=b²², bx=w, cx=av, dx=abu, ex=abt, fx=ab²t, gx=ab²s, hx=ab³s, ix=ab³r, jx=ab⁴r, kx=ab⁴q, lx=ab⁵q, mx=ab⁵p, nx=ab⁶p, ox=ab⁶o, px=ab⁷o, qx=ab⁷n, rx=ab⁸n, sx=ab⁸m, tx=ab⁹m, ux=b²¹, vx=b²², wx=b²¹, x²=b²²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², ae, abf, ag, ab²g, abh, ab³h, ai, ab²i, ab⁴i, abj, ab³j, ab⁵j, ak, ab²k, ab⁴k, ab⁶k, abl, ab³l, ab⁵l, ab⁷l, am, ab²m, ab⁴m, ab⁶m, ab⁸m, abn, ab³n, ab⁵n, ab⁷n, ao, ab²o, ab⁴o, ab⁶o, abp, ab³p, ab⁵p, aq, ab²q, ab⁴q, abr, ab³r, as, ab²s, abt, au, aw}

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 b²⁰ ab¹⁹ b²⁰ u b²¹ ab²⁰ b²¹ v b²² ab²¹ b²² w b²¹ ab²² b²¹ x b²² ab²¹ b²²

Monoid Structure