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 Q₁₁₁(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,y,z,A | a²=1, b²⁶=b²⁴, 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=b²³, l²=b²⁴, b¹⁰m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁵m, fm=ab⁶m, gm=ab⁷m, hm=ab⁸m, im=ab⁹m, jm=b²³, km=b²⁴, lm=b²⁵, m²=b²⁴, b¹¹n=ab²⁵, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=ab⁶n, gn=ab⁷n, hn=ab⁸n, in=ab⁹n, jn=ab¹⁰n, kn=b²⁵, ln=b²⁴, mn=b²⁵, n²=b²⁴, b¹¹o=b¹⁰n, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=ab⁶o, go=ab⁷o, ho=ab⁸o, io=ab⁹o, jo=ab¹⁰o, ko=ab¹⁰n, lo=b²⁵, mo=b²⁴, no=b²⁵, o²=b²⁴, b¹⁰p=b⁹o, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=ab⁶p, gp=ab⁷p, hp=ab⁸p, ip=ab⁹p, jp=ab⁹o, kp=ab¹⁰o, lp=ab¹⁰n, mp=b²⁵, np=b²⁴, op=b²⁵, p²=b²⁴, b⁹q=b⁸p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=ab⁶q, gq=ab⁷q, hq=ab⁸q, iq=ab⁸p, jq=ab⁹p, kq=ab⁹o, lq=ab¹⁰o, mq=ab¹⁰n, nq=b²⁵, oq=b²⁴, pq=b²⁵, q²=b²⁴, b⁸r=b⁷q, cr=ab²r, dr=ab⁴r, er=ab⁵r, fr=ab⁶r, gr=ab⁷r, hr=ab⁷q, ir=ab⁸q, jr=ab⁸p, kr=ab⁹p, lr=ab⁹o, mr=ab¹⁰o, nr=ab¹⁰n, or=b²⁵, pr=b²⁴, qr=b²⁵, r²=b²⁴, b⁷s=b⁶r, cs=ab²s, ds=ab⁴s, es=ab⁵s, fs=ab⁶s, gs=ab⁶r, hs=ab⁷r, is=ab⁷q, js=ab⁸q, ks=ab⁸p, ls=ab⁹p, ms=ab⁹o, ns=ab¹⁰o, os=ab¹⁰n, ps=b²⁵, qs=b²⁴, rs=b²⁵, s²=b²⁴, b⁶t=b⁵s, ct=ab²t, dt=ab⁴t, et=ab⁵t, ft=ab⁵s, gt=ab⁶s, ht=ab⁶r, it=ab⁷r, jt=ab⁷q, kt=ab⁸q, lt=ab⁸p, mt=ab⁹p, nt=ab⁹o, ot=ab¹⁰o, pt=ab¹⁰n, qt=b²⁵, rt=b²⁴, st=b²⁵, t²=b²⁴, b⁵u=b⁴t, cu=ab²u, du=ab⁴u, eu=ab⁴t, fu=ab⁵t, gu=ab⁵s, hu=ab⁶s, iu=ab⁶r, ju=ab⁷r, ku=ab⁷q, lu=ab⁸q, mu=ab⁸p, nu=ab⁹p, ou=ab⁹o, pu=ab¹⁰o, qu=ab¹⁰n, ru=b²⁵, su=b²⁴, tu=b²⁵, u²=b²⁴, b⁴v=b³u, cv=ab²v, dv=ab³u, ev=ab⁴u, fv=ab⁴t, gv=ab⁵t, hv=ab⁵s, iv=ab⁶s, jv=ab⁶r, kv=ab⁷r, lv=ab⁷q, mv=ab⁸q, nv=ab⁸p, ov=ab⁹p, pv=ab⁹o, qv=ab¹⁰o, rv=ab¹⁰n, sv=b²⁵, tv=b²⁴, uv=b²⁵, v²=b²⁴, b³w=b²v, cw=ab²w, dw=ab³v, ew=ab³u, fw=ab⁴u, gw=ab⁴t, hw=ab⁵t, iw=ab⁵s, jw=ab⁶s, kw=ab⁶r, lw=ab⁷r, mw=ab⁷q, nw=ab⁸q, ow=ab⁸p, pw=ab⁹p, qw=ab⁹o, rw=ab¹⁰o, sw=ab¹⁰n, tw=b²⁵, uw=b²⁴, vw=b²⁵, w²=b²⁴, b²x=bw, cx=abw, dx=ab²v, ex=ab³v, fx=ab³u, gx=ab⁴u, hx=ab⁴t, ix=ab⁵t, jx=ab⁵s, kx=ab⁶s, lx=ab⁶r, mx=ab⁷r, nx=ab⁷q, ox=ab⁸q, px=ab⁸p, qx=ab⁹p, rx=ab⁹o, sx=ab¹⁰o, tx=ab¹⁰n, ux=b²⁵, vx=b²⁴, wx=b²⁵, x²=b²⁴, by=x, cy=abx, dy=ab²w, ey=ab²v, fy=ab³v, gy=ab³u, hy=ab⁴u, iy=ab⁴t, jy=ab⁵t, ky=ab⁵s, ly=ab⁶s, my=ab⁶r, ny=ab⁷r, oy=ab⁷q, py=ab⁸q, qy=ab⁸p, ry=ab⁹p, sy=ab⁹o, ty=ab¹⁰o, uy=ab¹⁰n, vy=b²⁵, wy=b²⁴, xy=b²⁵, y²=b²⁴, bz=y, cz=ax, dz=abw, ez=ab²w, fz=ab²v, gz=ab³v, hz=ab³u, iz=ab⁴u, jz=ab⁴t, kz=ab⁵t, lz=ab⁵s, mz=ab⁶s, nz=ab⁶r, oz=ab⁷r, pz=ab⁷q, qz=ab⁸q, rz=ab⁸p, sz=ab⁹p, tz=ab⁹o, uz=ab¹⁰o, vz=ab¹⁰n, wz=b²⁵, xz=b²⁴, yz=b²⁵, z²=b²⁴, bA=z, cA=ay, dA=abx, eA=abw, fA=ab²w, gA=ab²v, hA=ab³v, iA=ab³u, jA=ab⁴u, kA=ab⁴t, lA=ab⁵t, mA=ab⁵s, nA=ab⁶s, oA=ab⁶r, pA=ab⁷r, qA=ab⁷q, rA=ab⁸q, sA=ab⁸p, tA=ab⁹p, uA=ab⁹o, vA=ab¹⁰o, wA=ab¹⁰n, xA=b²⁵, yA=b²⁴, zA=b²⁵, A²=b²⁴>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, 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, ab⁹n, ao, ab²o, ab⁴o, ab⁶o, ab⁸o, ab¹⁰o, abp, ab³p, ab⁵p, ab⁷p, ab⁹p, aq, ab²q, ab⁴q, ab⁶q, ab⁸q, abr, ab³r, ab⁵r, ab⁷r, as, ab²s, ab⁴s, ab⁶s, abt, ab³t, ab⁵t, au, ab²u, ab⁴u, abv, ab³v, aw, ab²w, abx, ay, aA}

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 b²³ ab²² b²³ x b²⁴ ab²³ b²⁴ y b²⁵ ab²⁴ b²⁵ z b²⁴ ab²⁵ b²⁴ A b²⁵ ab²⁴ b²⁵

Monoid Structure