Details Page for 0.7072

Complete Solution is Known:

MSV File: q-0.7072.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₈(0.7072):

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=b⁹, cf=ab²f, df=ab¹⁰, ef=ab¹¹, f²=b¹², b⁴g=ab¹¹, cg=ab²g, dg=b¹¹, eg=b¹², fg=ab¹³, g²=b¹⁴, b⁵h=b¹³, ch=ab²h, dh=ab⁴h, eh=ab¹³, fh=b¹⁴, gh=ab¹⁵, h²=b¹⁶, b⁶i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=ab⁵i, fi=ab¹⁵, gi=b¹⁶, hi=ab¹⁷, i²=b¹⁸, b⁷j=b¹⁷, cj=ab²j, dj=ab⁴j, ej=ab⁵j, fj=b⁶j, gj=ab¹⁷, hj=b¹⁸, ij=ab¹⁹, j²=b¹⁸, b⁸k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁵k, fk=b⁶k, gk=ab⁷k, hk=ab¹⁹, ik=b¹⁸, jk=ab¹⁹, k²=b¹⁸, b⁸l=ab⁷k, cl=ab²l, dl=ab⁴l, el=ab⁵l, fl=b⁶l, gl=ab⁷l, hl=ab⁷k, il=ab¹⁹, jl=b¹⁸, kl=ab¹⁹, l²=b¹⁸, b⁷m=ab⁶l, cm=ab²m, dm=ab⁴m, em=ab⁵m, fm=b⁶m, gm=b⁶l, hm=ab⁷l, im=ab⁷k, jm=ab¹⁹, km=b¹⁸, lm=ab¹⁹, m²=b¹⁸, b⁶n=ab⁵m, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=ab⁵m, gn=b⁶m, hn=b⁶l, in=ab⁷l, jn=ab⁷k, kn=ab¹⁹, ln=b¹⁸, mn=ab¹⁹, n²=b¹⁸, b⁵o=ab⁴n, co=ab²o, do=ab⁴o, eo=b⁴n, fo=ab⁵n, go=ab⁵m, ho=b⁶m, io=b⁶l, jo=ab⁷l, ko=ab⁷k, lo=ab¹⁹, mo=b¹⁸, no=ab¹⁹, o²=b¹⁸, b⁴p=ab³o, cp=ab²p, dp=b³o, ep=b⁴o, fp=b⁴n, gp=ab⁵n, hp=ab⁵m, ip=b⁶m, jp=b⁶l, kp=ab⁷l, lp=ab⁷k, mp=ab¹⁹, np=b¹⁸, op=ab¹⁹, p²=b¹⁸, b³q=ab²p, cq=ab²q, dq=b³p, eq=ab³o, fq=b⁴o, gq=b⁴n, hq=ab⁵n, iq=ab⁵m, jq=b⁶m, kq=b⁶l, lq=ab⁷l, mq=ab⁷k, nq=ab¹⁹, oq=b¹⁸, pq=ab¹⁹, q²=b¹⁸, b²r=abq, cr=bq, dr=ab²p, er=ab³p, fr=ab³o, gr=b⁴o, hr=b⁴n, ir=ab⁵n, jr=ab⁵m, kr=b⁶m, lr=b⁶l, mr=ab⁷l, nr=ab⁷k, or=ab¹⁹, pr=b¹⁸, qr=ab¹⁹, r²=b¹⁸, bs=ar, cs=br, ds=ab²q, es=b²p, fs=ab³p, gs=ab³o, hs=b⁴o, is=b⁴n, js=ab⁵n, ks=ab⁵m, ls=b⁶m, ms=b⁶l, ns=ab⁷l, os=ab⁷k, ps=ab¹⁹, qs=b¹⁸, rs=ab¹⁹, s²=b¹⁸, bt=as, ct=ar, dt=bq, et=b²q, ft=b²p, gt=ab³p, ht=ab³o, it=b⁴o, jt=b⁴n, kt=ab⁵n, lt=ab⁵m, mt=b⁶m, nt=b⁶l, ot=ab⁷l, pt=ab⁷k, qt=ab¹⁹, rt=b¹⁸, st=ab¹⁹, t²=b¹⁸, bu=at, cu=as, du=br, eu=abq, fu=b²q, gu=b²p, hu=ab³p, iu=ab³o, ju=b⁴o, ku=b⁴n, lu=ab⁵n, mu=ab⁵m, nu=b⁶m, ou=b⁶l, pu=ab⁷l, qu=ab⁷k, ru=ab¹⁹, su=b¹⁸, tu=ab¹⁹, u²=b¹⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, e, abf, g, b²g, abh, ab³h, i, b²i, b⁴i, abj, ab³j, ab⁵j, k, b²k, b⁴k, b⁶k, abl, ab³l, ab⁵l, ab⁷l, m, b²m, b⁴m, b⁶m, abn, ab³n, ab⁵n, o, b²o, b⁴o, abp, ab³p, q, b²q, abr, s, u}

Phi = 1 a 1 a 1 b ab b ab a 1 c ac b ab b³ ab³ c b² d ad b³ ab³ b⁵ e ab⁴ b⁴ ab⁶ f b⁵ ab⁵ b⁷ g ab⁶ b⁶ ab⁸ h b⁷ ab⁷ b⁹ i ab⁸ b⁸ ab¹⁰ j b⁹ ab⁹ b¹¹ k ab¹⁰ b¹⁰ ab¹² l b¹¹ ab¹¹ b¹³ m ab¹² b¹² ab¹⁴ n b¹³ ab¹³ b¹⁵ o ab¹⁴ b¹⁴ ab¹⁶ p b¹⁵ ab¹⁵ b¹⁷ q ab¹⁶ b¹⁶ ab¹⁸ r b¹⁷ ab¹⁷ b¹⁹ s ab¹⁸ b¹⁸ ab¹⁸ t b¹⁹ ab¹⁹ b¹⁹ u ab¹⁸ b¹⁸ ab¹⁸

Monoid Structure