Details Page for 0.7052

Complete Solution is Known:

MSV File: q-0.7052.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₀₈(0.7052):

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, b²⁵=b²³, 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=ab²³, m²=b²⁴, b¹¹n=b²³, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=b⁶n, gn=ab⁷n, hn=b⁸n, in=ab⁹n, jn=b¹⁰n, kn=ab²³, ln=b²⁴, mn=ab²³, n²=b²⁴, b¹⁰o=ab⁹n, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=b⁶o, go=ab⁷o, ho=b⁸o, io=ab⁹o, jo=ab⁹n, ko=b¹⁰n, lo=ab²³, mo=b²⁴, no=ab²³, o²=b²⁴, b⁹p=ab⁸o, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=b⁶p, gp=ab⁷p, hp=b⁸p, ip=b⁸o, jp=ab⁹o, kp=ab⁹n, lp=b¹⁰n, mp=ab²³, np=b²⁴, op=ab²³, p²=b²⁴, b⁸q=ab⁷p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=b⁶q, gq=ab⁷q, hq=ab⁷p, iq=b⁸p, jq=b⁸o, kq=ab⁹o, lq=ab⁹n, mq=b¹⁰n, nq=ab²³, oq=b²⁴, pq=ab²³, q²=b²⁴, b⁷r=ab⁶q, cr=ab²r, dr=ab⁴r, er=ab⁵r, fr=b⁶r, gr=b⁶q, hr=ab⁷q, ir=ab⁷p, jr=b⁸p, kr=b⁸o, lr=ab⁹o, mr=ab⁹n, nr=b¹⁰n, or=ab²³, pr=b²⁴, qr=ab²³, r²=b²⁴, b⁶s=ab⁵r, cs=ab²s, ds=ab⁴s, es=ab⁵s, fs=ab⁵r, gs=b⁶r, hs=b⁶q, is=ab⁷q, js=ab⁷p, ks=b⁸p, ls=b⁸o, ms=ab⁹o, ns=ab⁹n, os=b¹⁰n, ps=ab²³, qs=b²⁴, rs=ab²³, s²=b²⁴, b⁵t=ab⁴s, ct=ab²t, dt=ab⁴t, et=b⁴s, ft=ab⁵s, gt=ab⁵r, ht=b⁶r, it=b⁶q, jt=ab⁷q, kt=ab⁷p, lt=b⁸p, mt=b⁸o, nt=ab⁹o, ot=ab⁹n, pt=b¹⁰n, qt=ab²³, rt=b²⁴, st=ab²³, t²=b²⁴, b⁴u=ab³t, cu=ab²u, du=b³t, eu=b⁴t, fu=b⁴s, gu=ab⁵s, hu=ab⁵r, iu=b⁶r, ju=b⁶q, ku=ab⁷q, lu=ab⁷p, mu=b⁸p, nu=b⁸o, ou=ab⁹o, pu=ab⁹n, qu=b¹⁰n, ru=ab²³, su=b²⁴, tu=ab²³, u²=b²⁴, b³v=ab²u, cv=ab²v, dv=b³u, ev=ab³t, fv=b⁴t, gv=b⁴s, hv=ab⁵s, iv=ab⁵r, jv=b⁶r, kv=b⁶q, lv=ab⁷q, mv=ab⁷p, nv=b⁸p, ov=b⁸o, pv=ab⁹o, qv=ab⁹n, rv=b¹⁰n, sv=ab²³, tv=b²⁴, uv=ab²³, v²=b²⁴, b²w=abv, cw=bv, dw=ab²u, ew=ab³u, fw=ab³t, gw=b⁴t, hw=b⁴s, iw=ab⁵s, jw=ab⁵r, kw=b⁶r, lw=b⁶q, mw=ab⁷q, nw=ab⁷p, ow=b⁸p, pw=b⁸o, qw=ab⁹o, rw=ab⁹n, sw=b¹⁰n, tw=ab²³, uw=b²⁴, vw=ab²³, w²=b²⁴, bx=aw, cx=bw, dx=ab²v, ex=b²u, fx=ab³u, gx=ab³t, hx=b⁴t, ix=b⁴s, jx=ab⁵s, kx=ab⁵r, lx=b⁶r, mx=b⁶q, nx=ab⁷q, ox=ab⁷p, px=b⁸p, qx=b⁸o, rx=ab⁹o, sx=ab⁹n, tx=b¹⁰n, ux=ab²³, vx=b²⁴, wx=ab²³, x²=b²⁴, by=ax, cy=aw, dy=bv, ey=b²v, fy=b²u, gy=ab³u, hy=ab³t, iy=b⁴t, jy=b⁴s, ky=ab⁵s, ly=ab⁵r, my=b⁶r, ny=b⁶q, oy=ab⁷q, py=ab⁷p, qy=b⁸p, ry=b⁸o, sy=ab⁹o, ty=ab⁹n, uy=b¹⁰n, vy=ab²³, wy=b²⁴, xy=ab²³, y²=b²⁴, bz=ay, cz=ax, dz=bw, ez=abv, fz=b²v, gz=b²u, hz=ab³u, iz=ab³t, jz=b⁴t, kz=b⁴s, lz=ab⁵s, mz=ab⁵r, nz=b⁶r, oz=b⁶q, pz=ab⁷q, qz=ab⁷p, rz=b⁸p, sz=b⁸o, tz=ab⁹o, uz=ab⁹n, vz=b¹⁰n, wz=ab²³, xz=b²⁴, yz=ab²³, z²=b²⁴>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, 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, abp, ab³p, ab⁵p, ab⁷p, q, b²q, b⁴q, b⁶q, abr, ab³r, ab⁵r, s, b²s, b⁴s, abt, ab³t, u, b²u, abv, w, y}

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 b²³ y ab²⁴ b²⁴ ab²⁴ z b²³ ab²³ b²³

Monoid Structure