Details Page for 0.2224

Complete Solution is Known:

MSV File: q-0.2224.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₀(0.2224):

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, b²⁴=b²², bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, be=ab⁷, ce=b⁸, de=b¹⁰, e²=b¹², b²f=ab⁹, cf=b⁹, df=b¹¹, ef=b¹³, f²=b¹⁴, b³g=ab¹¹, cg=ab²g, dg=b¹², eg=b¹⁴, fg=b¹⁵, g²=b¹⁶, b⁴h=ab¹³, ch=ab²h, dh=b¹³, eh=b¹⁵, fh=b¹⁶, gh=b¹⁷, h²=b¹⁸, b⁵i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=b¹⁶, fi=b¹⁷, gi=b¹⁸, hi=b¹⁹, i²=b²⁰, b⁶j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b¹⁷, fj=b¹⁸, gj=b¹⁹, hj=b²⁰, ij=b²¹, j²=b²², b⁷k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁶k, fk=b¹⁹, gk=b²⁰, hk=b²¹, ik=b²², jk=b²³, k²=b²², b⁸l=ab²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=ab⁷l, gl=b²¹, hl=b²², il=b²³, jl=b²², kl=b²³, l²=b²², b⁹m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=ab⁷m, gm=ab⁸m, hm=b²³, im=b²², jm=b²³, km=b²², lm=b²³, m²=b²², b⁹n=b⁸m, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=ab⁷n, gn=ab⁸n, hn=ab⁸m, in=b²³, jn=b²², kn=b²³, ln=b²², mn=b²³, n²=b²², b⁸o=b⁷n, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=ab⁷o, go=ab⁷n, ho=ab⁸n, io=ab⁸m, jo=b²³, ko=b²², lo=b²³, mo=b²², no=b²³, o²=b²², b⁷p=b⁶o, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=ab⁶o, gp=ab⁷o, hp=ab⁷n, ip=ab⁸n, jp=ab⁸m, kp=b²³, lp=b²², mp=b²³, np=b²², op=b²³, p²=b²², b⁶q=b⁵p, cq=ab²q, dq=ab⁴q, eq=ab⁵p, fq=ab⁶p, gq=ab⁶o, hq=ab⁷o, iq=ab⁷n, jq=ab⁸n, kq=ab⁸m, lq=b²³, mq=b²², nq=b²³, oq=b²², pq=b²³, q²=b²², b⁵r=b⁴q, cr=ab²r, dr=ab⁴r, er=ab⁵q, fr=ab⁵p, gr=ab⁶p, hr=ab⁶o, ir=ab⁷o, jr=ab⁷n, kr=ab⁸n, lr=ab⁸m, mr=b²³, nr=b²², or=b²³, pr=b²², qr=b²³, r²=b²², b⁴s=b³r, cs=ab²s, ds=ab³r, es=ab⁴q, fs=ab⁵q, gs=ab⁵p, hs=ab⁶p, is=ab⁶o, js=ab⁷o, ks=ab⁷n, ls=ab⁸n, ms=ab⁸m, ns=b²³, os=b²², ps=b²³, qs=b²², rs=b²³, s²=b²², b³t=b²s, ct=ab²t, dt=ab³s, et=ab⁴r, ft=ab⁴q, gt=ab⁵q, ht=ab⁵p, it=ab⁶p, jt=ab⁶o, kt=ab⁷o, lt=ab⁷n, mt=ab⁸n, nt=ab⁸m, ot=b²³, pt=b²², qt=b²³, rt=b²², st=b²³, t²=b²², b²u=bt, cu=abt, du=ab²s, eu=ab³r, fu=ab⁴r, gu=ab⁴q, hu=ab⁵q, iu=ab⁵p, ju=ab⁶p, ku=ab⁶o, lu=ab⁷o, mu=ab⁷n, nu=ab⁸n, ou=ab⁸m, pu=b²³, qu=b²², ru=b²³, su=b²², tu=b²³, u²=b²², bv=u, cv=abu, dv=ab²t, ev=ab³s, fv=ab³r, gv=ab⁴r, hv=ab⁴q, iv=ab⁵q, jv=ab⁵p, kv=ab⁶p, lv=ab⁶o, mv=ab⁷o, nv=ab⁷n, ov=ab⁸n, pv=ab⁸m, qv=b²³, rv=b²², sv=b²³, tv=b²², uv=b²³, v²=b²², bw=v, cw=au, dw=abt, ew=ab²s, fw=ab³s, gw=ab³r, hw=ab⁴r, iw=ab⁴q, jw=ab⁵q, kw=ab⁵p, lw=ab⁶p, mw=ab⁶o, nw=ab⁷o, ow=ab⁷n, pw=ab⁸n, qw=ab⁸m, rw=b²³, sw=b²², tw=b²³, uw=b²², vw=b²³, w²=b²², bx=w, cx=av, dx=abu, ex=ab²t, fx=ab²s, gx=ab³s, hx=ab³r, ix=ab⁴r, jx=ab⁴q, kx=ab⁵q, lx=ab⁵p, mx=ab⁶p, nx=ab⁶o, ox=ab⁷o, px=ab⁷n, qx=ab⁸n, rx=ab⁸m, sx=b²³, tx=b²², ux=b²³, vx=b²², wx=b²³, x²=b²², by=x, cy=aw, dy=au, ey=abt, fy=ab²t, gy=ab²s, hy=ab³s, iy=ab³r, jy=ab⁴r, ky=ab⁴q, ly=ab⁵q, my=ab⁵p, ny=ab⁶p, oy=ab⁶o, py=ab⁷o, qy=ab⁷n, ry=ab⁸n, sy=ab⁸m, ty=b²³, uy=b²², vy=b²³, wy=b²², xy=b²³, y²=b²², bz=y, cz=ax, dz=av, ez=abu, fz=abt, gz=ab²t, hz=ab²s, iz=ab³s, jz=ab³r, kz=ab⁴r, lz=ab⁴q, mz=ab⁵q, nz=ab⁵p, oz=ab⁶p, pz=ab⁶o, qz=ab⁷o, rz=ab⁷n, sz=ab⁸n, tz=ab⁸m, uz=b²³, vz=b²², wz=b²³, xz=b²², yz=b²³, z²=b²²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², af, abg, ah, ab²h, abi, ab³i, aj, ab²j, ab⁴j, abk, ab³k, ab⁵k, al, ab²l, ab⁴l, ab⁶l, abm, ab³m, ab⁵m, ab⁷m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, abo, ab³o, ab⁵o, ab⁷o, ap, ab²p, ab⁴p, ab⁶p, abq, ab³q, ab⁵q, ar, ab²r, ab⁴r, abs, ab³s, at, ab²t, abu, av, ax, az}

Phi = 1 1 a b ab 1 a b ab 1 c b ab³ b² d b³ ab⁵ b⁴ e b⁵ f b⁶ g b⁷ h b⁸ i b⁹ j b¹⁰ k b¹¹ l b¹² m b¹³ n b¹⁴ o b¹⁵ p b¹⁶ q b¹⁷ r b¹⁸ s b¹⁹ t b²⁰ u b²¹ v b²² w b²³ x b²² y b²³ z b²²

Monoid Structure