Details Page for 0.7153

Complete Solution is Known:

MSV File: q-0.7153.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₁₃(0.7153):

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,B | a²=1, b²⁹=b²⁷, bc=ab³, c²=b⁴, b²d=ab⁵, cd=b⁵, d²=b⁶, b³e=ab⁷, ce=ab²e, de=b⁷, e²=b⁸, b⁴f=ab⁹, cf=ab²f, df=ab³f, ef=b⁹, f²=b¹⁰, b⁵g=ab¹¹, cg=ab²g, dg=ab³g, eg=ab⁴g, fg=b¹¹, g²=b¹², b⁶h=ab¹³, ch=ab²h, dh=ab³h, eh=ab⁴h, fh=ab⁵h, gh=b¹³, h²=b¹⁴, b⁷i=ab¹⁵, ci=ab²i, di=ab³i, ei=ab⁴i, fi=ab⁵i, gi=ab⁶i, hi=b¹⁵, i²=b¹⁶, b⁸j=ab¹⁷, cj=ab²j, dj=ab³j, ej=ab⁴j, fj=ab⁵j, gj=ab⁶j, hj=ab⁷j, ij=b¹⁷, j²=b¹⁸, b⁹k=ab¹⁹, ck=ab²k, dk=ab³k, ek=ab⁴k, fk=ab⁵k, gk=ab⁶k, hk=ab⁷k, ik=ab⁸k, jk=b¹⁹, k²=b²⁰, b¹⁰l=ab²¹, cl=ab²l, dl=ab³l, el=ab⁴l, fl=ab⁵l, gl=ab⁶l, hl=ab⁷l, il=ab⁸l, jl=ab⁹l, kl=b²¹, l²=b²², b¹¹m=ab²³, cm=ab²m, dm=ab³m, em=ab⁴m, fm=ab⁵m, gm=ab⁶m, hm=ab⁷m, im=ab⁸m, jm=ab⁹m, km=ab¹⁰m, lm=b²³, m²=b²⁴, b¹²n=ab²⁵, cn=ab²n, dn=ab³n, en=ab⁴n, fn=ab⁵n, gn=ab⁶n, hn=ab⁷n, in=ab⁸n, jn=ab⁹n, kn=ab¹⁰n, ln=ab¹¹n, mn=b²⁵, n²=b²⁶, b¹³o=ab²⁷, co=ab²o, do=ab³o, eo=ab⁴o, fo=ab⁵o, go=ab⁶o, ho=ab⁷o, io=ab⁸o, jo=ab⁹o, ko=ab¹⁰o, lo=ab¹¹o, mo=ab¹²o, no=b²⁷, o²=b²⁸, b¹⁴p=ab²⁷, cp=ab²p, dp=ab³p, ep=ab⁴p, fp=ab⁵p, gp=ab⁶p, hp=ab⁷p, ip=ab⁸p, jp=ab⁹p, kp=ab¹⁰p, lp=ab¹¹p, mp=ab¹²p, np=ab¹³p, op=b²⁷, p²=b²⁸, b¹³q=b¹²p, cq=ab²q, dq=ab³q, eq=ab⁴q, fq=ab⁵q, gq=ab⁶q, hq=ab⁷q, iq=ab⁸q, jq=ab⁹q, kq=ab¹⁰q, lq=ab¹¹q, mq=ab¹²q, nq=ab¹²p, oq=ab¹³p, pq=b²⁷, q²=b²⁸, b¹²r=b¹¹q, cr=ab²r, dr=ab³r, er=ab⁴r, fr=ab⁵r, gr=ab⁶r, hr=ab⁷r, ir=ab⁸r, jr=ab⁹r, kr=ab¹⁰r, lr=ab¹¹r, mr=ab¹¹q, nr=ab¹²q, or=ab¹²p, pr=ab¹³p, qr=b²⁷, r²=b²⁸, b¹¹s=b¹⁰r, cs=ab²s, ds=ab³s, es=ab⁴s, fs=ab⁵s, gs=ab⁶s, hs=ab⁷s, is=ab⁸s, js=ab⁹s, ks=ab¹⁰s, ls=ab¹⁰r, ms=ab¹¹r, ns=ab¹¹q, os=ab¹²q, ps=ab¹²p, qs=ab¹³p, rs=b²⁷, s²=b²⁸, b¹⁰t=b⁹s, ct=ab²t, dt=ab³t, et=ab⁴t, ft=ab⁵t, gt=ab⁶t, ht=ab⁷t, it=ab⁸t, jt=ab⁹t, kt=ab⁹s, lt=ab¹⁰s, mt=ab¹⁰r, nt=ab¹¹r, ot=ab¹¹q, pt=ab¹²q, qt=ab¹²p, rt=ab¹³p, st=b²⁷, t²=b²⁸, b⁹u=b⁸t, cu=ab²u, du=ab³u, eu=ab⁴u, fu=ab⁵u, gu=ab⁶u, hu=ab⁷u, iu=ab⁸u, ju=ab⁸t, ku=ab⁹t, lu=ab⁹s, mu=ab¹⁰s, nu=ab¹⁰r, ou=ab¹¹r, pu=ab¹¹q, qu=ab¹²q, ru=ab¹²p, su=ab¹³p, tu=b²⁷, u²=b²⁸, b⁸v=b⁷u, cv=ab²v, dv=ab³v, ev=ab⁴v, fv=ab⁵v, gv=ab⁶v, hv=ab⁷v, iv=ab⁷u, jv=ab⁸u, kv=ab⁸t, lv=ab⁹t, mv=ab⁹s, nv=ab¹⁰s, ov=ab¹⁰r, pv=ab¹¹r, qv=ab¹¹q, rv=ab¹²q, sv=ab¹²p, tv=ab¹³p, uv=b²⁷, v²=b²⁸, b⁷w=b⁶v, cw=ab²w, dw=ab³w, ew=ab⁴w, fw=ab⁵w, gw=ab⁶w, hw=ab⁶v, iw=ab⁷v, jw=ab⁷u, kw=ab⁸u, lw=ab⁸t, mw=ab⁹t, nw=ab⁹s, ow=ab¹⁰s, pw=ab¹⁰r, qw=ab¹¹r, rw=ab¹¹q, sw=ab¹²q, tw=ab¹²p, uw=ab¹³p, vw=b²⁷, w²=b²⁸, b⁶x=b⁵w, cx=ab²x, dx=ab³x, ex=ab⁴x, fx=ab⁵x, gx=ab⁵w, hx=ab⁶w, ix=ab⁶v, jx=ab⁷v, kx=ab⁷u, lx=ab⁸u, mx=ab⁸t, nx=ab⁹t, ox=ab⁹s, px=ab¹⁰s, qx=ab¹⁰r, rx=ab¹¹r, sx=ab¹¹q, tx=ab¹²q, ux=ab¹²p, vx=ab¹³p, wx=b²⁷, x²=b²⁸, b⁵y=b⁴x, cy=ab²y, dy=ab³y, ey=ab⁴y, fy=ab⁴x, gy=ab⁵x, hy=ab⁵w, iy=ab⁶w, jy=ab⁶v, ky=ab⁷v, ly=ab⁷u, my=ab⁸u, ny=ab⁸t, oy=ab⁹t, py=ab⁹s, qy=ab¹⁰s, ry=ab¹⁰r, sy=ab¹¹r, ty=ab¹¹q, uy=ab¹²q, vy=ab¹²p, wy=ab¹³p, xy=b²⁷, y²=b²⁸, b⁴z=b³y, cz=ab²z, dz=ab³z, ez=ab³y, fz=ab⁴y, gz=ab⁴x, hz=ab⁵x, iz=ab⁵w, jz=ab⁶w, kz=ab⁶v, lz=ab⁷v, mz=ab⁷u, nz=ab⁸u, oz=ab⁸t, pz=ab⁹t, qz=ab⁹s, rz=ab¹⁰s, sz=ab¹⁰r, tz=ab¹¹r, uz=ab¹¹q, vz=ab¹²q, wz=ab¹²p, xz=ab¹³p, yz=b²⁷, z²=b²⁸, b³A=b²z, cA=ab²A, dA=ab²z, eA=ab³z, fA=ab³y, gA=ab⁴y, hA=ab⁴x, iA=ab⁵x, jA=ab⁵w, kA=ab⁶w, lA=ab⁶v, mA=ab⁷v, nA=ab⁷u, oA=ab⁸u, pA=ab⁸t, qA=ab⁹t, rA=ab⁹s, sA=ab¹⁰s, tA=ab¹⁰r, uA=ab¹¹r, vA=ab¹¹q, wA=ab¹²q, xA=ab¹²p, yA=ab¹³p, zA=b²⁷, A²=b²⁸, b³B=bA, cB=ab²B, dB=abA, eB=ab²A, fB=ab²z, gB=ab³z, hB=ab³y, iB=ab⁴y, jB=ab⁴x, kB=ab⁵x, lB=ab⁵w, mB=ab⁶w, nB=ab⁶v, oB=ab⁷v, pB=ab⁷u, qB=ab⁸u, rB=ab⁸t, sB=ab⁹t, tB=ab⁹s, uB=ab¹⁰s, vB=ab¹⁰r, wB=ab¹¹r, xB=ab¹¹q, yB=ab¹²q, zB=ab¹²p, AB=ab¹³p, B²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, ad, abe, af, ab²f, abg, ab³g, ah, ab²h, ab⁴h, abi, ab³i, ab⁵i, aj, ab²j, ab⁴j, ab⁶j, abk, ab³k, ab⁵k, ab⁷k, al, ab²l, ab⁴l, ab⁶l, ab⁸l, abm, ab³m, ab⁵m, ab⁷m, ab⁹m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, ab¹⁰n, abo, ab³o, ab⁵o, ab⁷o, ab⁹o, ab¹¹o, ap, ab²p, ab⁴p, ab⁶p, ab⁸p, ab¹⁰p, ab¹²p, abq, ab³q, ab⁵q, ab⁷q, ab⁹q, ab¹¹q, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, ab¹⁰r, abs, ab³s, ab⁵s, ab⁷s, ab⁹s, at, ab²t, ab⁴t, ab⁶t, ab⁸t, abu, ab³u, ab⁵u, ab⁷u, av, ab²v, ab⁴v, ab⁶v, abw, ab³w, ab⁵w, ax, ab²x, ab⁴x, aby, ab³y, az, ab²z, abA, abB}

Phi = 1 a b a b ab b² ab b² c 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 A b²⁷ ab²⁶ b²⁷ bB b²⁸ ab²⁷ b²⁸ B b²⁷ ab²⁸ b²⁷

Monoid Structure