Details Page for 0.5143

Complete Solution is Known:

MSV File: q-0.5143.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₀₀(0.5143):

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=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b³f=ab⁹, cf=ab²f, df=b¹⁰, ef=ab¹¹, f²=b¹², b⁴g=b¹¹, cg=ab²g, dg=ab¹¹, eg=b¹², fg=ab¹³, g²=b¹⁴, b⁵h=ab¹³, ch=ab²h, dh=ab⁴h, eh=ab¹³, fh=b¹⁴, gh=ab¹⁵, h²=b¹⁶, b⁶i=b¹⁵, ci=ab²i, di=ab⁴i, ei=b⁵i, fi=ab¹⁵, gi=b¹⁶, hi=ab¹⁷, i²=b¹⁸, b⁷j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁶j, gj=ab¹⁷, hj=b¹⁸, ij=ab¹⁹, j²=b²⁰, b⁸k=b¹⁹, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁶k, gk=b⁷k, hk=ab¹⁹, ik=b²⁰, jk=ab²¹, k²=b²², b⁹l=ab²¹, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁶l, gl=b⁷l, hl=ab⁸l, il=ab²¹, jl=b²², kl=ab²¹, l²=b²², b¹⁰m=b²¹, cm=ab²m, dm=ab⁴m, em=b⁵m, fm=ab⁶m, gm=b⁷m, hm=ab⁸m, im=b⁹m, jm=ab²¹, km=b²², lm=ab²¹, m²=b²², b⁹n=ab⁸m, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁶n, gn=b⁷n, hn=ab⁸n, in=ab⁸m, jn=b⁹m, kn=ab²¹, ln=b²², mn=ab²¹, n²=b²², b⁸o=ab⁷n, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁶o, go=b⁷o, ho=b⁷n, io=ab⁸n, jo=ab⁸m, ko=b⁹m, lo=ab²¹, mo=b²², no=ab²¹, o²=b²², b⁷p=ab⁶o, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁶p, gp=ab⁶o, hp=b⁷o, ip=b⁷n, jp=ab⁸n, kp=ab⁸m, lp=b⁹m, mp=ab²¹, np=b²², op=ab²¹, p²=b²², b⁶q=ab⁵p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=b⁵p, gq=ab⁶p, hq=ab⁶o, iq=b⁷o, jq=b⁷n, kq=ab⁸n, lq=ab⁸m, mq=b⁹m, nq=ab²¹, oq=b²², pq=ab²¹, q²=b²², b⁵r=ab⁴q, cr=ab²r, dr=ab⁴r, er=ab⁴q, fr=b⁵q, gr=b⁵p, hr=ab⁶p, ir=ab⁶o, jr=b⁷o, kr=b⁷n, lr=ab⁸n, mr=ab⁸m, nr=b⁹m, or=ab²¹, pr=b²², qr=ab²¹, r²=b²², b⁴s=ab³r, cs=ab²s, ds=b³r, es=ab⁴r, fs=ab⁴q, gs=b⁵q, hs=b⁵p, is=ab⁶p, js=ab⁶o, ks=b⁷o, ls=b⁷n, ms=ab⁸n, ns=ab⁸m, os=b⁹m, ps=ab²¹, qs=b²², rs=ab²¹, s²=b²², b³t=ab²s, ct=ab²t, dt=b³s, et=b³r, ft=ab⁴r, gt=ab⁴q, ht=b⁵q, it=b⁵p, jt=ab⁶p, kt=ab⁶o, lt=b⁷o, mt=b⁷n, nt=ab⁸n, ot=ab⁸m, pt=b⁹m, qt=ab²¹, rt=b²², st=ab²¹, t²=b²², b²u=abt, cu=bt, du=ab²s, eu=b³s, fu=b³r, gu=ab⁴r, hu=ab⁴q, iu=b⁵q, ju=b⁵p, ku=ab⁶p, lu=ab⁶o, mu=b⁷o, nu=b⁷n, ou=ab⁸n, pu=ab⁸m, qu=b⁹m, ru=ab²¹, su=b²², tu=ab²¹, u²=b²², bv=au, cv=bu, dv=ab²t, ev=ab²s, fv=b³s, gv=b³r, hv=ab⁴r, iv=ab⁴q, jv=b⁵q, kv=b⁵p, lv=ab⁶p, mv=ab⁶o, nv=b⁷o, ov=b⁷n, pv=ab⁸n, qv=ab⁸m, rv=b⁹m, sv=ab²¹, tv=b²², uv=ab²¹, v²=b²², bw=av, cw=au, dw=bt, ew=ab²t, fw=ab²s, gw=b³s, hw=b³r, iw=ab⁴r, jw=ab⁴q, kw=b⁵q, lw=b⁵p, mw=ab⁶p, nw=ab⁶o, ow=b⁷o, pw=b⁷n, qw=ab⁸n, rw=ab⁸m, sw=b⁹m, tw=ab²¹, uw=b²², vw=ab²¹, w²=b²², bx=aw, cx=av, dx=bu, ex=bt, fx=ab²t, gx=ab²s, hx=b³s, ix=b³r, jx=ab⁴r, kx=ab⁴q, lx=b⁵q, mx=b⁵p, nx=ab⁶p, ox=ab⁶o, px=b⁷o, qx=b⁷n, rx=ab⁸n, sx=ab⁸m, tx=b⁹m, ux=ab²¹, vx=b²², wx=ab²¹, x²=b²²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², ae, bf, ag, ab²g, bh, b³h, ai, ab²i, ab⁴i, bj, b³j, b⁵j, ak, ab²k, ab⁴k, ab⁶k, bl, b³l, b⁵l, b⁷l, am, ab²m, ab⁴m, ab⁶m, ab⁸m, bn, b³n, b⁵n, b⁷n, ao, ab²o, ab⁴o, ab⁶o, bp, b³p, b⁵p, aq, ab²q, ab⁴q, br, b³r, as, ab²s, bt, au, aw}

Phi = 1 a a a a b b b b a a c c b b b³ b³ c ab² d d b³ b³ b⁵ e ab⁴ ab⁴ ab⁶ f b⁵ b⁵ b⁷ g ab⁶ ab⁶ ab⁸ h b⁷ b⁷ b⁹ i ab⁸ ab⁸ ab¹⁰ j b⁹ b⁹ b¹¹ k ab¹⁰ ab¹⁰ ab¹² l b¹¹ b¹¹ b¹³ m ab¹² ab¹² ab¹⁴ n b¹³ b¹³ b¹⁵ o ab¹⁴ ab¹⁴ ab¹⁶ p b¹⁵ b¹⁵ b¹⁷ q ab¹⁶ ab¹⁶ ab¹⁸ r b¹⁷ b¹⁷ b¹⁹ s ab¹⁸ ab¹⁸ ab²⁰ t b¹⁹ b¹⁹ b²¹ u ab²⁰ ab²⁰ ab²² v b²¹ b²¹ b²¹ w ab²² ab²² ab²² x b²¹ b²¹ b²¹

Monoid Structure