Details Page for 0.7072

Complete Solution is Known:

MSV File: q-0.7072.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₁₆(0.7072):

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 | a²=1, b²⁷=b²⁵, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, b²e=ab⁷, ce=b⁷, de=b⁹, e²=b¹⁰, b³f=b⁹, cf=ab²f, df=ab¹⁰, ef=ab¹¹, f²=b¹², b⁴g=ab¹¹, cg=ab²g, dg=b¹¹, eg=b¹², fg=ab¹³, g²=b¹⁴, b⁵h=b¹³, ch=ab²h, dh=ab⁴h, eh=ab¹³, fh=b¹⁴, gh=ab¹⁵, h²=b¹⁶, b⁶i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=ab⁵i, fi=ab¹⁵, gi=b¹⁶, hi=ab¹⁷, i²=b¹⁸, b⁷j=b¹⁷, cj=ab²j, dj=ab⁴j, ej=ab⁵j, fj=b⁶j, gj=ab¹⁷, hj=b¹⁸, ij=ab¹⁹, j²=b²⁰, b⁸k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁵k, fk=b⁶k, gk=ab⁷k, hk=ab¹⁹, ik=b²⁰, jk=ab²¹, k²=b²², b⁹l=b²¹, cl=ab²l, dl=ab⁴l, el=ab⁵l, fl=b⁶l, gl=ab⁷l, hl=b⁸l, il=ab²¹, jl=b²², kl=ab²³, l²=b²⁴, b¹⁰m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁵m, fm=b⁶m, gm=ab⁷m, hm=b⁸m, im=ab⁹m, jm=ab²³, km=b²⁴, lm=ab²⁵, m²=b²⁶, b¹¹n=b²⁵, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=b⁶n, gn=ab⁷n, hn=b⁸n, in=ab⁹n, jn=b¹⁰n, kn=ab²⁵, ln=b²⁶, mn=ab²⁵, n²=b²⁶, b¹²o=ab²⁵, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=b⁶o, go=ab⁷o, ho=b⁸o, io=ab⁹o, jo=b¹⁰o, ko=ab¹¹o, lo=ab²⁵, mo=b²⁶, no=ab²⁵, o²=b²⁶, b¹¹p=ab¹⁰o, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=b⁶p, gp=ab⁷p, hp=b⁸p, ip=ab⁹p, jp=b¹⁰p, kp=b¹⁰o, lp=ab¹¹o, mp=ab²⁵, np=b²⁶, op=ab²⁵, p²=b²⁶, b¹⁰q=ab⁹p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=b⁶q, gq=ab⁷q, hq=b⁸q, iq=ab⁹q, jq=ab⁹p, kq=b¹⁰p, lq=b¹⁰o, mq=ab¹¹o, nq=ab²⁵, oq=b²⁶, pq=ab²⁵, q²=b²⁶, b⁹r=ab⁸q, cr=ab²r, dr=ab⁴r, er=ab⁵r, fr=b⁶r, gr=ab⁷r, hr=b⁸r, ir=b⁸q, jr=ab⁹q, kr=ab⁹p, lr=b¹⁰p, mr=b¹⁰o, nr=ab¹¹o, or=ab²⁵, pr=b²⁶, qr=ab²⁵, r²=b²⁶, b⁸s=ab⁷r, cs=ab²s, ds=ab⁴s, es=ab⁵s, fs=b⁶s, gs=ab⁷s, hs=ab⁷r, is=b⁸r, js=b⁸q, ks=ab⁹q, ls=ab⁹p, ms=b¹⁰p, ns=b¹⁰o, os=ab¹¹o, ps=ab²⁵, qs=b²⁶, rs=ab²⁵, s²=b²⁶, b⁷t=ab⁶s, ct=ab²t, dt=ab⁴t, et=ab⁵t, ft=b⁶t, gt=b⁶s, ht=ab⁷s, it=ab⁷r, jt=b⁸r, kt=b⁸q, lt=ab⁹q, mt=ab⁹p, nt=b¹⁰p, ot=b¹⁰o, pt=ab¹¹o, qt=ab²⁵, rt=b²⁶, st=ab²⁵, t²=b²⁶, b⁶u=ab⁵t, cu=ab²u, du=ab⁴u, eu=ab⁵u, fu=ab⁵t, gu=b⁶t, hu=b⁶s, iu=ab⁷s, ju=ab⁷r, ku=b⁸r, lu=b⁸q, mu=ab⁹q, nu=ab⁹p, ou=b¹⁰p, pu=b¹⁰o, qu=ab¹¹o, ru=ab²⁵, su=b²⁶, tu=ab²⁵, u²=b²⁶, b⁵v=ab⁴u, cv=ab²v, dv=ab⁴v, ev=b⁴u, fv=ab⁵u, gv=ab⁵t, hv=b⁶t, iv=b⁶s, jv=ab⁷s, kv=ab⁷r, lv=b⁸r, mv=b⁸q, nv=ab⁹q, ov=ab⁹p, pv=b¹⁰p, qv=b¹⁰o, rv=ab¹¹o, sv=ab²⁵, tv=b²⁶, uv=ab²⁵, v²=b²⁶, b⁴w=ab³v, cw=ab²w, dw=b³v, ew=b⁴v, fw=b⁴u, gw=ab⁵u, hw=ab⁵t, iw=b⁶t, jw=b⁶s, kw=ab⁷s, lw=ab⁷r, mw=b⁸r, nw=b⁸q, ow=ab⁹q, pw=ab⁹p, qw=b¹⁰p, rw=b¹⁰o, sw=ab¹¹o, tw=ab²⁵, uw=b²⁶, vw=ab²⁵, w²=b²⁶, b³x=ab²w, cx=ab²x, dx=b³w, ex=ab³v, fx=b⁴v, gx=b⁴u, hx=ab⁵u, ix=ab⁵t, jx=b⁶t, kx=b⁶s, lx=ab⁷s, mx=ab⁷r, nx=b⁸r, ox=b⁸q, px=ab⁹q, qx=ab⁹p, rx=b¹⁰p, sx=b¹⁰o, tx=ab¹¹o, ux=ab²⁵, vx=b²⁶, wx=ab²⁵, x²=b²⁶, b²y=abx, cy=bx, dy=ab²w, ey=ab³w, fy=ab³v, gy=b⁴v, hy=b⁴u, iy=ab⁵u, jy=ab⁵t, ky=b⁶t, ly=b⁶s, my=ab⁷s, ny=ab⁷r, oy=b⁸r, py=b⁸q, qy=ab⁹q, ry=ab⁹p, sy=b¹⁰p, ty=b¹⁰o, uy=ab¹¹o, vy=ab²⁵, wy=b²⁶, xy=ab²⁵, y²=b²⁶, b³z=ay, cz=ab²z, dz=by, ez=abx, fz=b²x, gz=b²w, hz=ab³w, iz=ab³v, jz=b⁴v, kz=b⁴u, lz=ab⁵u, mz=ab⁵t, nz=b⁶t, oz=b⁶s, pz=ab⁷s, qz=ab⁷r, rz=b⁸r, sz=b⁸q, tz=ab⁹q, uz=ab⁹p, vz=b¹⁰p, wz=b¹⁰o, xz=ab¹¹o, yz=ab²⁵, z²=b²⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, e, abf, g, b²g, abh, ab³h, i, b²i, b⁴i, abj, ab³j, ab⁵j, k, b²k, b⁴k, b⁶k, abl, ab³l, ab⁵l, ab⁷l, m, b²m, b⁴m, b⁶m, b⁸m, abn, ab³n, ab⁵n, ab⁷n, ab⁹n, o, b²o, b⁴o, b⁶o, b⁸o, b¹⁰o, abp, ab³p, ab⁵p, ab⁷p, ab⁹p, q, b²q, b⁴q, b⁶q, b⁸q, abr, ab³r, ab⁵r, ab⁷r, s, b²s, b⁴s, b⁶s, abt, ab³t, ab⁵t, u, b²u, b⁴u, abv, ab³v, w, b²w, abx, y, abz}

Phi = 1 a 1 a 1 b ab b ab a 1 c ac b ab b³ ab³ c b² d ad b³ ab³ b⁵ e ab⁴ b⁴ ab⁶ f b⁵ ab⁵ b⁷ g ab⁶ b⁶ ab⁸ h b⁷ ab⁷ b⁹ i ab⁸ b⁸ ab¹⁰ j b⁹ ab⁹ b¹¹ k ab¹⁰ b¹⁰ ab¹² l b¹¹ ab¹¹ b¹³ m ab¹² b¹² ab¹⁴ n b¹³ ab¹³ b¹⁵ o ab¹⁴ b¹⁴ ab¹⁶ p b¹⁵ ab¹⁵ b¹⁷ q ab¹⁶ b¹⁶ ab¹⁸ r b¹⁷ ab¹⁷ b¹⁹ s ab¹⁸ b¹⁸ ab²⁰ t b¹⁹ ab¹⁹ b²¹ u ab²⁰ b²⁰ ab²² v b²¹ ab²¹ b²³ w ab²² b²² ab²⁴ x b²³ ab²³ b²⁵ y ab²⁴ b²⁴ ab²⁶ b²z b²⁵ ab²⁵ b²⁵ abz ab²⁶ b²⁶ ab²⁶ z b²⁵ ab²⁵ b²⁵

Monoid Structure