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 Q₇₀(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, b²⁹=b²⁷, 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=b²⁸, b¹⁰n=ab²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=ab⁷n, gn=ab⁸n, hn=ab⁹n, in=b²⁵, jn=b²⁶, kn=b²⁷, ln=b²⁸, mn=b²⁷, n²=b²⁸, b¹¹o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=ab⁷o, go=ab⁸o, ho=ab⁹o, io=ab¹⁰o, jo=b²⁷, ko=b²⁸, lo=b²⁷, mo=b²⁸, no=b²⁷, o²=b²⁸, b¹²p=ab²⁷, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=ab⁷p, gp=ab⁸p, hp=ab⁹p, ip=ab¹⁰p, jp=ab¹¹p, kp=b²⁷, lp=b²⁸, mp=b²⁷, np=b²⁸, op=b²⁷, p²=b²⁸, b¹¹q=b¹⁰p, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=ab⁷q, gq=ab⁸q, hq=ab⁹q, iq=ab¹⁰q, jq=ab¹⁰p, kq=ab¹¹p, lq=b²⁷, mq=b²⁸, nq=b²⁷, oq=b²⁸, pq=b²⁷, q²=b²⁸, b¹⁰r=b⁹q, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=ab⁷r, gr=ab⁸r, hr=ab⁹r, ir=ab⁹q, jr=ab¹⁰q, kr=ab¹⁰p, lr=ab¹¹p, mr=b²⁷, nr=b²⁸, or=b²⁷, pr=b²⁸, qr=b²⁷, r²=b²⁸, b⁹s=b⁸r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=ab⁷s, gs=ab⁸s, hs=ab⁸r, is=ab⁹r, js=ab⁹q, ks=ab¹⁰q, ls=ab¹⁰p, ms=ab¹¹p, ns=b²⁷, os=b²⁸, ps=b²⁷, qs=b²⁸, rs=b²⁷, s²=b²⁸, b⁸t=b⁷s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=ab⁷t, gt=ab⁷s, ht=ab⁸s, it=ab⁸r, jt=ab⁹r, kt=ab⁹q, lt=ab¹⁰q, mt=ab¹⁰p, nt=ab¹¹p, ot=b²⁷, pt=b²⁸, qt=b²⁷, rt=b²⁸, st=b²⁷, t²=b²⁸, b⁷u=b⁶t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=ab⁶t, gu=ab⁷t, hu=ab⁷s, iu=ab⁸s, ju=ab⁸r, ku=ab⁹r, lu=ab⁹q, mu=ab¹⁰q, nu=ab¹⁰p, ou=ab¹¹p, pu=b²⁷, qu=b²⁸, ru=b²⁷, su=b²⁸, tu=b²⁷, u²=b²⁸, b⁶v=b⁵u, cv=ab²v, dv=ab⁴v, ev=ab⁵u, fv=ab⁶u, gv=ab⁶t, hv=ab⁷t, iv=ab⁷s, jv=ab⁸s, kv=ab⁸r, lv=ab⁹r, mv=ab⁹q, nv=ab¹⁰q, ov=ab¹⁰p, pv=ab¹¹p, qv=b²⁷, rv=b²⁸, sv=b²⁷, tv=b²⁸, uv=b²⁷, v²=b²⁸, b⁵w=b⁴v, cw=ab²w, dw=ab⁴w, ew=ab⁵v, fw=ab⁵u, gw=ab⁶u, hw=ab⁶t, iw=ab⁷t, jw=ab⁷s, kw=ab⁸s, lw=ab⁸r, mw=ab⁹r, nw=ab⁹q, ow=ab¹⁰q, pw=ab¹⁰p, qw=ab¹¹p, rw=b²⁷, sw=b²⁸, tw=b²⁷, uw=b²⁸, vw=b²⁷, w²=b²⁸, b⁴x=b³w, cx=ab²x, dx=ab³w, ex=ab⁴v, fx=ab⁵v, gx=ab⁵u, hx=ab⁶u, ix=ab⁶t, jx=ab⁷t, kx=ab⁷s, lx=ab⁸s, mx=ab⁸r, nx=ab⁹r, ox=ab⁹q, px=ab¹⁰q, qx=ab¹⁰p, rx=ab¹¹p, sx=b²⁷, tx=b²⁸, ux=b²⁷, vx=b²⁸, wx=b²⁷, x²=b²⁸, b³y=b²x, cy=ab²y, dy=ab³x, ey=ab⁴w, fy=ab⁴v, gy=ab⁵v, hy=ab⁵u, iy=ab⁶u, jy=ab⁶t, ky=ab⁷t, ly=ab⁷s, my=ab⁸s, ny=ab⁸r, oy=ab⁹r, py=ab⁹q, qy=ab¹⁰q, ry=ab¹⁰p, sy=ab¹¹p, ty=b²⁷, uy=b²⁸, vy=b²⁷, wy=b²⁸, xy=b²⁷, y²=b²⁸, b²z=by, cz=aby, dz=ab²x, ez=ab³w, fz=ab⁴w, gz=ab⁴v, hz=ab⁵v, iz=ab⁵u, jz=ab⁶u, kz=ab⁶t, lz=ab⁷t, mz=ab⁷s, nz=ab⁸s, oz=ab⁸r, pz=ab⁹r, qz=ab⁹q, rz=ab¹⁰q, sz=ab¹⁰p, tz=ab¹¹p, uz=b²⁷, vz=b²⁸, wz=b²⁷, xz=b²⁸, yz=b²⁷, z²=b²⁸, bA=z, cA=abz, dA=ab²y, eA=ab³x, fA=ab³w, gA=ab⁴w, hA=ab⁴v, iA=ab⁵v, jA=ab⁵u, kA=ab⁶u, lA=ab⁶t, mA=ab⁷t, nA=ab⁷s, oA=ab⁸s, pA=ab⁸r, qA=ab⁹r, rA=ab⁹q, sA=ab¹⁰q, tA=ab¹⁰p, uA=ab¹¹p, vA=b²⁷, wA=b²⁸, xA=b²⁷, yA=b²⁸, zA=b²⁷, A²=b²⁸, bB=A, cB=az, dB=aby, eB=ab²x, fB=ab³x, gB=ab³w, hB=ab⁴w, iB=ab⁴v, jB=ab⁵v, kB=ab⁵u, lB=ab⁶u, mB=ab⁶t, nB=ab⁷t, oB=ab⁷s, pB=ab⁸s, qB=ab⁸r, rB=ab⁹r, sB=ab⁹q, tB=ab¹⁰q, uB=ab¹⁰p, vB=ab¹¹p, wB=b²⁷, xB=b²⁸, yB=b²⁷, zB=b²⁸, AB=b²⁷, B²=b²⁸, b³C=B, cC=ab²C, dC=aA, eC=abz, fC=aby, gC=ab²y, hC=ab²x, iC=ab³x, jC=ab³w, kC=ab⁴w, lC=ab⁴v, mC=ab⁵v, nC=ab⁵u, oC=ab⁶u, pC=ab⁶t, qC=ab⁷t, rC=ab⁷s, sC=ab⁸s, tC=ab⁸r, uC=ab⁹r, vC=ab⁹q, wC=ab¹⁰q, xC=ab¹⁰p, yC=ab¹¹p, zC=b²⁷, AC=b²⁸, BC=b²⁷, C²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, 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, abC}

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 b²⁸ b²C b²⁷ bC b²⁸ C b²⁷

Monoid Structure