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 Q₁₁₉(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, b²⁸=b²⁶, 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=b²⁶, b¹²o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=ab⁶o, go=ab⁷o, ho=ab⁸o, io=ab⁹o, jo=ab¹⁰o, ko=ab¹¹o, lo=b²⁷, mo=b²⁶, no=b²⁷, o²=b²⁶, b¹²p=b¹¹o, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=ab⁶p, gp=ab⁷p, hp=ab⁸p, ip=ab⁹p, jp=ab¹⁰p, kp=ab¹¹p, lp=ab¹¹o, mp=b²⁷, np=b²⁶, op=b²⁷, p²=b²⁶, b¹¹q=b¹⁰p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=ab⁶q, gq=ab⁷q, hq=ab⁸q, iq=ab⁹q, jq=ab¹⁰q, kq=ab¹⁰p, lq=ab¹¹p, mq=ab¹¹o, nq=b²⁷, oq=b²⁶, pq=b²⁷, q²=b²⁶, b¹⁰r=b⁹q, cr=ab²r, dr=ab⁴r, er=ab⁵r, fr=ab⁶r, gr=ab⁷r, hr=ab⁸r, ir=ab⁹r, jr=ab⁹q, kr=ab¹⁰q, lr=ab¹⁰p, mr=ab¹¹p, nr=ab¹¹o, or=b²⁷, pr=b²⁶, qr=b²⁷, r²=b²⁶, b⁹s=b⁸r, cs=ab²s, ds=ab⁴s, es=ab⁵s, fs=ab⁶s, gs=ab⁷s, hs=ab⁸s, is=ab⁸r, js=ab⁹r, ks=ab⁹q, ls=ab¹⁰q, ms=ab¹⁰p, ns=ab¹¹p, os=ab¹¹o, ps=b²⁷, qs=b²⁶, rs=b²⁷, s²=b²⁶, b⁸t=b⁷s, ct=ab²t, dt=ab⁴t, et=ab⁵t, ft=ab⁶t, gt=ab⁷t, ht=ab⁷s, it=ab⁸s, jt=ab⁸r, kt=ab⁹r, lt=ab⁹q, mt=ab¹⁰q, nt=ab¹⁰p, ot=ab¹¹p, pt=ab¹¹o, qt=b²⁷, rt=b²⁶, st=b²⁷, t²=b²⁶, b⁷u=b⁶t, cu=ab²u, du=ab⁴u, eu=ab⁵u, fu=ab⁶u, gu=ab⁶t, hu=ab⁷t, iu=ab⁷s, ju=ab⁸s, ku=ab⁸r, lu=ab⁹r, mu=ab⁹q, nu=ab¹⁰q, ou=ab¹⁰p, pu=ab¹¹p, qu=ab¹¹o, ru=b²⁷, su=b²⁶, tu=b²⁷, u²=b²⁶, b⁶v=b⁵u, cv=ab²v, dv=ab⁴v, ev=ab⁵v, fv=ab⁵u, gv=ab⁶u, hv=ab⁶t, iv=ab⁷t, jv=ab⁷s, kv=ab⁸s, lv=ab⁸r, mv=ab⁹r, nv=ab⁹q, ov=ab¹⁰q, pv=ab¹⁰p, qv=ab¹¹p, rv=ab¹¹o, sv=b²⁷, tv=b²⁶, uv=b²⁷, v²=b²⁶, b⁵w=b⁴v, cw=ab²w, dw=ab⁴w, ew=ab⁴v, fw=ab⁵v, gw=ab⁵u, hw=ab⁶u, iw=ab⁶t, jw=ab⁷t, kw=ab⁷s, lw=ab⁸s, mw=ab⁸r, nw=ab⁹r, ow=ab⁹q, pw=ab¹⁰q, qw=ab¹⁰p, rw=ab¹¹p, sw=ab¹¹o, tw=b²⁷, uw=b²⁶, vw=b²⁷, w²=b²⁶, b⁴x=b³w, cx=ab²x, dx=ab³w, ex=ab⁴w, fx=ab⁴v, gx=ab⁵v, hx=ab⁵u, ix=ab⁶u, jx=ab⁶t, kx=ab⁷t, lx=ab⁷s, mx=ab⁸s, nx=ab⁸r, ox=ab⁹r, px=ab⁹q, qx=ab¹⁰q, rx=ab¹⁰p, sx=ab¹¹p, tx=ab¹¹o, ux=b²⁷, vx=b²⁶, wx=b²⁷, x²=b²⁶, b³y=b²x, cy=ab²y, dy=ab³x, ey=ab³w, fy=ab⁴w, gy=ab⁴v, hy=ab⁵v, iy=ab⁵u, jy=ab⁶u, ky=ab⁶t, ly=ab⁷t, my=ab⁷s, ny=ab⁸s, oy=ab⁸r, py=ab⁹r, qy=ab⁹q, ry=ab¹⁰q, sy=ab¹⁰p, ty=ab¹¹p, uy=ab¹¹o, vy=b²⁷, wy=b²⁶, xy=b²⁷, y²=b²⁶, b²z=by, cz=aby, dz=ab²x, ez=ab³x, fz=ab³w, gz=ab⁴w, hz=ab⁴v, iz=ab⁵v, jz=ab⁵u, kz=ab⁶u, lz=ab⁶t, mz=ab⁷t, nz=ab⁷s, oz=ab⁸s, pz=ab⁸r, qz=ab⁹r, rz=ab⁹q, sz=ab¹⁰q, tz=ab¹⁰p, uz=ab¹¹p, vz=ab¹¹o, wz=b²⁷, xz=b²⁶, yz=b²⁷, z²=b²⁶, b³A=z, cA=ab²A, dA=abz, eA=aby, fA=ab²y, gA=ab²x, hA=ab³x, iA=ab³w, jA=ab⁴w, kA=ab⁴v, lA=ab⁵v, mA=ab⁵u, nA=ab⁶u, oA=ab⁶t, pA=ab⁷t, qA=ab⁷s, rA=ab⁸s, sA=ab⁸r, tA=ab⁹r, uA=ab⁹q, vA=ab¹⁰q, wA=ab¹⁰p, xA=ab¹¹p, yA=ab¹¹o, zA=b²⁷, 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, 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, aA, ab²A}

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 b²A b²⁷ ab²⁶ b²⁷ bA b²⁶ ab²⁷ b²⁶ A b²⁷ ab²⁶ b²⁷

Monoid Structure