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 Q₁₁₅(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, b²⁷=b²⁵, 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=b²⁶, b¹¹n=ab²⁵, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=ab⁶n, gn=ab⁷n, hn=ab⁸n, in=ab⁹n, jn=ab¹⁰n, kn=b²⁵, ln=b²⁶, mn=b²⁵, n²=b²⁶, b¹²o=ab²⁵, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=ab⁶o, go=ab⁷o, ho=ab⁸o, io=ab⁹o, jo=ab¹⁰o, ko=ab¹¹o, lo=b²⁵, mo=b²⁶, no=b²⁵, o²=b²⁶, b¹¹p=b¹⁰o, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=ab⁶p, gp=ab⁷p, hp=ab⁸p, ip=ab⁹p, jp=ab¹⁰p, kp=ab¹⁰o, lp=ab¹¹o, mp=b²⁵, np=b²⁶, op=b²⁵, p²=b²⁶, b¹⁰q=b⁹p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=ab⁶q, gq=ab⁷q, hq=ab⁸q, iq=ab⁹q, jq=ab⁹p, kq=ab¹⁰p, lq=ab¹⁰o, mq=ab¹¹o, nq=b²⁵, oq=b²⁶, pq=b²⁵, q²=b²⁶, b⁹r=b⁸q, cr=ab²r, dr=ab⁴r, er=ab⁵r, fr=ab⁶r, gr=ab⁷r, hr=ab⁸r, ir=ab⁸q, jr=ab⁹q, kr=ab⁹p, lr=ab¹⁰p, mr=ab¹⁰o, nr=ab¹¹o, or=b²⁵, pr=b²⁶, qr=b²⁵, r²=b²⁶, b⁸s=b⁷r, cs=ab²s, ds=ab⁴s, es=ab⁵s, fs=ab⁶s, gs=ab⁷s, hs=ab⁷r, is=ab⁸r, js=ab⁸q, ks=ab⁹q, ls=ab⁹p, ms=ab¹⁰p, ns=ab¹⁰o, os=ab¹¹o, ps=b²⁵, qs=b²⁶, rs=b²⁵, s²=b²⁶, b⁷t=b⁶s, ct=ab²t, dt=ab⁴t, et=ab⁵t, ft=ab⁶t, gt=ab⁶s, ht=ab⁷s, it=ab⁷r, jt=ab⁸r, kt=ab⁸q, lt=ab⁹q, mt=ab⁹p, nt=ab¹⁰p, ot=ab¹⁰o, pt=ab¹¹o, qt=b²⁵, rt=b²⁶, st=b²⁵, t²=b²⁶, b⁶u=b⁵t, cu=ab²u, du=ab⁴u, eu=ab⁵u, fu=ab⁵t, gu=ab⁶t, hu=ab⁶s, iu=ab⁷s, ju=ab⁷r, ku=ab⁸r, lu=ab⁸q, mu=ab⁹q, nu=ab⁹p, ou=ab¹⁰p, pu=ab¹⁰o, qu=ab¹¹o, ru=b²⁵, su=b²⁶, tu=b²⁵, u²=b²⁶, b⁵v=b⁴u, cv=ab²v, dv=ab⁴v, ev=ab⁴u, fv=ab⁵u, gv=ab⁵t, hv=ab⁶t, iv=ab⁶s, jv=ab⁷s, kv=ab⁷r, lv=ab⁸r, mv=ab⁸q, nv=ab⁹q, ov=ab⁹p, pv=ab¹⁰p, qv=ab¹⁰o, rv=ab¹¹o, sv=b²⁵, tv=b²⁶, uv=b²⁵, v²=b²⁶, b⁴w=b³v, cw=ab²w, dw=ab³v, ew=ab⁴v, fw=ab⁴u, gw=ab⁵u, hw=ab⁵t, iw=ab⁶t, jw=ab⁶s, kw=ab⁷s, lw=ab⁷r, mw=ab⁸r, nw=ab⁸q, ow=ab⁹q, pw=ab⁹p, qw=ab¹⁰p, rw=ab¹⁰o, sw=ab¹¹o, tw=b²⁵, uw=b²⁶, vw=b²⁵, w²=b²⁶, b³x=b²w, cx=ab²x, dx=ab³w, ex=ab³v, fx=ab⁴v, gx=ab⁴u, hx=ab⁵u, ix=ab⁵t, jx=ab⁶t, kx=ab⁶s, lx=ab⁷s, mx=ab⁷r, nx=ab⁸r, ox=ab⁸q, px=ab⁹q, qx=ab⁹p, rx=ab¹⁰p, sx=ab¹⁰o, tx=ab¹¹o, ux=b²⁵, vx=b²⁶, wx=b²⁵, x²=b²⁶, b²y=bx, cy=abx, dy=ab²w, ey=ab³w, fy=ab³v, gy=ab⁴v, hy=ab⁴u, iy=ab⁵u, jy=ab⁵t, ky=ab⁶t, ly=ab⁶s, my=ab⁷s, ny=ab⁷r, oy=ab⁸r, py=ab⁸q, qy=ab⁹q, ry=ab⁹p, sy=ab¹⁰p, ty=ab¹⁰o, uy=ab¹¹o, vy=b²⁵, wy=b²⁶, xy=b²⁵, y²=b²⁶, bz=y, cz=aby, dz=ab²x, ez=ab²w, fz=ab³w, gz=ab³v, hz=ab⁴v, iz=ab⁴u, jz=ab⁵u, kz=ab⁵t, lz=ab⁶t, mz=ab⁶s, nz=ab⁷s, oz=ab⁷r, pz=ab⁸r, qz=ab⁸q, rz=ab⁹q, sz=ab⁹p, tz=ab¹⁰p, uz=ab¹⁰o, vz=ab¹¹o, wz=b²⁵, xz=b²⁶, yz=b²⁵, z²=b²⁶, b²A=z, cA=az, dA=aby, eA=abx, fA=ab²x, gA=ab²w, hA=ab³w, iA=ab³v, jA=ab⁴v, kA=ab⁴u, lA=ab⁵u, mA=ab⁵t, nA=ab⁶t, oA=ab⁶s, pA=ab⁷s, qA=ab⁷r, rA=ab⁸r, sA=ab⁸q, tA=ab⁹q, uA=ab⁹p, vA=ab¹⁰p, wA=ab¹⁰o, xA=ab¹¹o, yA=b²⁵, zA=b²⁶, A²=b²⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, 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, abA}

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 b²⁶ ab²⁵ b²⁶ bA b²⁵ ab²⁶ b²⁵ A b²⁶ ab²⁵ b²⁶

Monoid Structure