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 Q₁₂₃(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, b²⁹=b²⁷, 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=b²⁷, n²=b²⁸, b¹²o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=ab⁶o, go=ab⁷o, ho=ab⁸o, io=ab⁹o, jo=ab¹⁰o, ko=ab¹¹o, lo=b²⁷, mo=b²⁸, no=b²⁷, o²=b²⁸, b¹³p=ab²⁷, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=ab⁶p, gp=ab⁷p, hp=ab⁸p, ip=ab⁹p, jp=ab¹⁰p, kp=ab¹¹p, lp=ab¹²p, mp=b²⁷, np=b²⁸, op=b²⁷, p²=b²⁸, b¹²q=b¹¹p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=ab⁶q, gq=ab⁷q, hq=ab⁸q, iq=ab⁹q, jq=ab¹⁰q, kq=ab¹¹q, lq=ab¹¹p, mq=ab¹²p, nq=b²⁷, oq=b²⁸, pq=b²⁷, q²=b²⁸, b¹¹r=b¹⁰q, cr=ab²r, dr=ab⁴r, er=ab⁵r, fr=ab⁶r, gr=ab⁷r, hr=ab⁸r, ir=ab⁹r, jr=ab¹⁰r, kr=ab¹⁰q, lr=ab¹¹q, mr=ab¹¹p, nr=ab¹²p, or=b²⁷, pr=b²⁸, qr=b²⁷, r²=b²⁸, b¹⁰s=b⁹r, cs=ab²s, ds=ab⁴s, es=ab⁵s, fs=ab⁶s, gs=ab⁷s, hs=ab⁸s, is=ab⁹s, js=ab⁹r, ks=ab¹⁰r, ls=ab¹⁰q, ms=ab¹¹q, ns=ab¹¹p, os=ab¹²p, ps=b²⁷, qs=b²⁸, rs=b²⁷, s²=b²⁸, b⁹t=b⁸s, ct=ab²t, dt=ab⁴t, et=ab⁵t, ft=ab⁶t, gt=ab⁷t, ht=ab⁸t, it=ab⁸s, jt=ab⁹s, kt=ab⁹r, lt=ab¹⁰r, mt=ab¹⁰q, nt=ab¹¹q, ot=ab¹¹p, pt=ab¹²p, qt=b²⁷, rt=b²⁸, st=b²⁷, t²=b²⁸, b⁸u=b⁷t, cu=ab²u, du=ab⁴u, eu=ab⁵u, fu=ab⁶u, gu=ab⁷u, hu=ab⁷t, iu=ab⁸t, ju=ab⁸s, ku=ab⁹s, lu=ab⁹r, mu=ab¹⁰r, nu=ab¹⁰q, ou=ab¹¹q, pu=ab¹¹p, qu=ab¹²p, ru=b²⁷, su=b²⁸, tu=b²⁷, u²=b²⁸, b⁷v=b⁶u, cv=ab²v, dv=ab⁴v, ev=ab⁵v, fv=ab⁶v, gv=ab⁶u, hv=ab⁷u, iv=ab⁷t, jv=ab⁸t, kv=ab⁸s, lv=ab⁹s, mv=ab⁹r, nv=ab¹⁰r, ov=ab¹⁰q, pv=ab¹¹q, qv=ab¹¹p, rv=ab¹²p, sv=b²⁷, tv=b²⁸, uv=b²⁷, v²=b²⁸, b⁶w=b⁵v, cw=ab²w, dw=ab⁴w, ew=ab⁵w, fw=ab⁵v, gw=ab⁶v, hw=ab⁶u, iw=ab⁷u, jw=ab⁷t, kw=ab⁸t, lw=ab⁸s, mw=ab⁹s, nw=ab⁹r, ow=ab¹⁰r, pw=ab¹⁰q, qw=ab¹¹q, rw=ab¹¹p, sw=ab¹²p, tw=b²⁷, uw=b²⁸, vw=b²⁷, w²=b²⁸, b⁵x=b⁴w, cx=ab²x, dx=ab⁴x, ex=ab⁴w, fx=ab⁵w, gx=ab⁵v, hx=ab⁶v, ix=ab⁶u, jx=ab⁷u, kx=ab⁷t, lx=ab⁸t, mx=ab⁸s, nx=ab⁹s, ox=ab⁹r, px=ab¹⁰r, qx=ab¹⁰q, rx=ab¹¹q, sx=ab¹¹p, tx=ab¹²p, ux=b²⁷, vx=b²⁸, wx=b²⁷, x²=b²⁸, b⁴y=b³x, cy=ab²y, dy=ab³x, ey=ab⁴x, fy=ab⁴w, gy=ab⁵w, hy=ab⁵v, iy=ab⁶v, jy=ab⁶u, ky=ab⁷u, ly=ab⁷t, my=ab⁸t, ny=ab⁸s, oy=ab⁹s, py=ab⁹r, qy=ab¹⁰r, ry=ab¹⁰q, sy=ab¹¹q, ty=ab¹¹p, uy=ab¹²p, vy=b²⁷, wy=b²⁸, xy=b²⁷, y²=b²⁸, b³z=b²y, cz=ab²z, dz=ab³y, ez=ab³x, fz=ab⁴x, gz=ab⁴w, hz=ab⁵w, iz=ab⁵v, jz=ab⁶v, kz=ab⁶u, lz=ab⁷u, mz=ab⁷t, nz=ab⁸t, oz=ab⁸s, pz=ab⁹s, qz=ab⁹r, rz=ab¹⁰r, sz=ab¹⁰q, tz=ab¹¹q, uz=ab¹¹p, vz=ab¹²p, wz=b²⁷, xz=b²⁸, yz=b²⁷, z²=b²⁸, b⁵A=bz, cA=ab²A, dA=ab⁴A, eA=abz, fA=ab²z, gA=ab²y, hA=ab³y, iA=ab³x, jA=ab⁴x, kA=ab⁴w, lA=ab⁵w, mA=ab⁵v, nA=ab⁶v, oA=ab⁶u, pA=ab⁷u, qA=ab⁷t, rA=ab⁸t, sA=ab⁸s, tA=ab⁹s, uA=ab⁹r, vA=ab¹⁰r, wA=ab¹⁰q, xA=ab¹¹q, yA=ab¹¹p, zA=ab¹²p, A²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, 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, ab¹¹p, aq, ab²q, ab⁴q, ab⁶q, ab⁸q, ab¹⁰q, abr, ab³r, ab⁵r, ab⁷r, ab⁹r, as, ab²s, ab⁴s, ab⁶s, ab⁸s, abt, ab³t, ab⁵t, ab⁷t, au, ab²u, ab⁴u, ab⁶u, abv, ab³v, ab⁵v, aw, ab²w, ab⁴w, abx, ab³x, ay, ab²y, abz, abA, ab³A}

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 b³A b²⁷ ab²⁶ b²⁷ b²A b²⁸ ab²⁷ b²⁸ bA b²⁷ ab²⁸ b²⁷ A b²⁸ ab²⁷ b²⁸

Monoid Structure