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 Q₆₈(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,A,B,C | a²=1, b²⁸=b²⁶, 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=b²⁴, b⁸l=ab²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=ab⁷l, gl=b²¹, hl=b²², il=b²³, jl=b²⁴, kl=b²⁵, l²=b²⁶, b⁹m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=ab⁷m, gm=ab⁸m, hm=b²³, im=b²⁴, jm=b²⁵, km=b²⁶, lm=b²⁷, m²=b²⁶, b¹⁰n=ab²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=ab⁷n, gn=ab⁸n, hn=ab⁹n, in=b²⁵, jn=b²⁶, kn=b²⁷, ln=b²⁶, mn=b²⁷, n²=b²⁶, b¹¹o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=ab⁷o, go=ab⁸o, ho=ab⁹o, io=ab¹⁰o, jo=b²⁷, ko=b²⁶, lo=b²⁷, mo=b²⁶, no=b²⁷, o²=b²⁶, b¹¹p=b¹⁰o, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=ab⁷p, gp=ab⁸p, hp=ab⁹p, ip=ab¹⁰p, jp=ab¹⁰o, kp=b²⁷, lp=b²⁶, mp=b²⁷, np=b²⁶, op=b²⁷, p²=b²⁶, b¹⁰q=b⁹p, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=ab⁷q, gq=ab⁸q, hq=ab⁹q, iq=ab⁹p, jq=ab¹⁰p, kq=ab¹⁰o, lq=b²⁷, mq=b²⁶, nq=b²⁷, oq=b²⁶, pq=b²⁷, q²=b²⁶, b⁹r=b⁸q, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=ab⁷r, gr=ab⁸r, hr=ab⁸q, ir=ab⁹q, jr=ab⁹p, kr=ab¹⁰p, lr=ab¹⁰o, mr=b²⁷, nr=b²⁶, or=b²⁷, pr=b²⁶, qr=b²⁷, r²=b²⁶, b⁸s=b⁷r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=ab⁷s, gs=ab⁷r, hs=ab⁸r, is=ab⁸q, js=ab⁹q, ks=ab⁹p, ls=ab¹⁰p, ms=ab¹⁰o, ns=b²⁷, os=b²⁶, ps=b²⁷, qs=b²⁶, rs=b²⁷, s²=b²⁶, b⁷t=b⁶s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=ab⁶s, gt=ab⁷s, ht=ab⁷r, it=ab⁸r, jt=ab⁸q, kt=ab⁹q, lt=ab⁹p, mt=ab¹⁰p, nt=ab¹⁰o, ot=b²⁷, pt=b²⁶, qt=b²⁷, rt=b²⁶, st=b²⁷, t²=b²⁶, b⁶u=b⁵t, cu=ab²u, du=ab⁴u, eu=ab⁵t, fu=ab⁶t, gu=ab⁶s, hu=ab⁷s, iu=ab⁷r, ju=ab⁸r, ku=ab⁸q, lu=ab⁹q, mu=ab⁹p, nu=ab¹⁰p, ou=ab¹⁰o, pu=b²⁷, qu=b²⁶, ru=b²⁷, su=b²⁶, tu=b²⁷, u²=b²⁶, b⁵v=b⁴u, cv=ab²v, dv=ab⁴v, ev=ab⁵u, fv=ab⁵t, gv=ab⁶t, hv=ab⁶s, iv=ab⁷s, jv=ab⁷r, kv=ab⁸r, lv=ab⁸q, mv=ab⁹q, nv=ab⁹p, ov=ab¹⁰p, pv=ab¹⁰o, qv=b²⁷, rv=b²⁶, sv=b²⁷, tv=b²⁶, uv=b²⁷, v²=b²⁶, b⁴w=b³v, cw=ab²w, dw=ab³v, ew=ab⁴u, fw=ab⁵u, gw=ab⁵t, hw=ab⁶t, iw=ab⁶s, jw=ab⁷s, kw=ab⁷r, lw=ab⁸r, mw=ab⁸q, nw=ab⁹q, ow=ab⁹p, pw=ab¹⁰p, qw=ab¹⁰o, rw=b²⁷, sw=b²⁶, tw=b²⁷, uw=b²⁶, vw=b²⁷, w²=b²⁶, b³x=b²w, cx=ab²x, dx=ab³w, ex=ab⁴v, fx=ab⁴u, gx=ab⁵u, hx=ab⁵t, ix=ab⁶t, jx=ab⁶s, kx=ab⁷s, lx=ab⁷r, mx=ab⁸r, nx=ab⁸q, ox=ab⁹q, px=ab⁹p, qx=ab¹⁰p, rx=ab¹⁰o, sx=b²⁷, tx=b²⁶, ux=b²⁷, vx=b²⁶, wx=b²⁷, x²=b²⁶, b²y=bx, cy=abx, dy=ab²w, ey=ab³v, fy=ab⁴v, gy=ab⁴u, hy=ab⁵u, iy=ab⁵t, jy=ab⁶t, ky=ab⁶s, ly=ab⁷s, my=ab⁷r, ny=ab⁸r, oy=ab⁸q, py=ab⁹q, qy=ab⁹p, ry=ab¹⁰p, sy=ab¹⁰o, ty=b²⁷, uy=b²⁶, vy=b²⁷, wy=b²⁶, xy=b²⁷, y²=b²⁶, bz=y, cz=aby, dz=ab²x, ez=ab³w, fz=ab³v, gz=ab⁴v, hz=ab⁴u, iz=ab⁵u, jz=ab⁵t, kz=ab⁶t, lz=ab⁶s, mz=ab⁷s, nz=ab⁷r, oz=ab⁸r, pz=ab⁸q, qz=ab⁹q, rz=ab⁹p, sz=ab¹⁰p, tz=ab¹⁰o, uz=b²⁷, vz=b²⁶, wz=b²⁷, xz=b²⁶, yz=b²⁷, z²=b²⁶, bA=z, cA=ay, dA=abx, eA=ab²w, fA=ab³w, gA=ab³v, hA=ab⁴v, iA=ab⁴u, jA=ab⁵u, kA=ab⁵t, lA=ab⁶t, mA=ab⁶s, nA=ab⁷s, oA=ab⁷r, pA=ab⁸r, qA=ab⁸q, rA=ab⁹q, sA=ab⁹p, tA=ab¹⁰p, uA=ab¹⁰o, vA=b²⁷, wA=b²⁶, xA=b²⁷, yA=b²⁶, zA=b²⁷, A²=b²⁶, bB=A, cB=az, dB=aby, eB=ab²x, fB=ab²w, gB=ab³w, hB=ab³v, iB=ab⁴v, jB=ab⁴u, kB=ab⁵u, lB=ab⁵t, mB=ab⁶t, nB=ab⁶s, oB=ab⁷s, pB=ab⁷r, qB=ab⁸r, rB=ab⁸q, sB=ab⁹q, tB=ab⁹p, uB=ab¹⁰p, vB=ab¹⁰o, wB=b²⁷, xB=b²⁶, yB=b²⁷, zB=b²⁶, AB=b²⁷, B²=b²⁶, b²C=B, cC=aB, dC=az, eC=aby, fC=abx, gC=ab²x, hC=ab²w, iC=ab³w, jC=ab³v, kC=ab⁴v, lC=ab⁴u, mC=ab⁵u, nC=ab⁵t, oC=ab⁶t, pC=ab⁶s, qC=ab⁷s, rC=ab⁷r, sC=ab⁸r, tC=ab⁸q, uC=ab⁹q, vC=ab⁹p, wC=ab¹⁰p, xC=ab¹⁰o, yC=b²⁷, zC=b²⁶, AC=b²⁷, BC=b²⁶, C²=b²⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, 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, ab⁹o, ap, ab²p, ab⁴p, ab⁶p, ab⁸p, ab¹⁰p, abq, ab³q, ab⁵q, ab⁷q, ab⁹q, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, abs, ab³s, ab⁵s, ab⁷s, at, ab²t, ab⁴t, ab⁶t, abu, ab³u, ab⁵u, av, ab²v, ab⁴v, abw, ab³w, ax, ab²x, aby, az, aB, aC}

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 b²⁴ y b²⁵ z b²⁶ A b²⁷ B b²⁶ bC b²⁷ C b²⁶

Monoid Structure