Details Page for 0.5161

Complete Solution is Known:

MSV File: q-0.5161.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₉₇(0.5161):

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 | a²=1, b²⁹=b²⁷, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, b²e=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b³f=ab⁹, cf=ab²f, df=b¹⁰, ef=ab¹¹, f²=b¹², b⁴g=b¹¹, cg=ab²g, dg=ab¹¹, eg=b¹², fg=ab¹³, g²=b¹⁴, b⁵h=ab¹³, ch=ab²h, dh=ab⁴h, eh=ab¹³, fh=b¹⁴, gh=ab¹⁵, h²=b¹⁶, b⁶i=b¹⁵, ci=ab²i, di=ab⁴i, ei=b⁵i, fi=ab¹⁵, gi=b¹⁶, hi=ab¹⁷, i²=b¹⁸, b⁷j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁶j, gj=ab¹⁷, hj=b¹⁸, ij=ab¹⁹, j²=b²⁰, b⁸k=b¹⁹, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁶k, gk=b⁷k, hk=ab¹⁹, ik=b²⁰, jk=ab²¹, k²=b²², b⁹l=ab²¹, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁶l, gl=b⁷l, hl=ab⁸l, il=ab²¹, jl=b²², kl=ab²³, l²=b²⁴, b¹⁰m=b²³, cm=ab²m, dm=ab⁴m, em=b⁵m, fm=ab⁶m, gm=b⁷m, hm=ab⁸m, im=b⁹m, jm=ab²³, km=b²⁴, lm=ab²⁵, m²=b²⁶, b¹¹n=ab²⁵, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁶n, gn=b⁷n, hn=ab⁸n, in=b⁹n, jn=ab¹⁰n, kn=ab²⁵, ln=b²⁶, mn=ab²⁷, n²=b²⁸, b¹²o=b²⁷, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁶o, go=b⁷o, ho=ab⁸o, io=b⁹o, jo=ab¹⁰o, ko=b¹¹o, lo=ab²⁷, mo=b²⁸, no=ab²⁷, o²=b²⁸, b¹³p=ab²⁷, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁶p, gp=b⁷p, hp=ab⁸p, ip=b⁹p, jp=ab¹⁰p, kp=b¹¹p, lp=ab¹²p, mp=ab²⁷, np=b²⁸, op=ab²⁷, p²=b²⁸, b¹²q=ab¹¹p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁶q, gq=b⁷q, hq=ab⁸q, iq=b⁹q, jq=ab¹⁰q, kq=b¹¹q, lq=b¹¹p, mq=ab¹²p, nq=ab²⁷, oq=b²⁸, pq=ab²⁷, q²=b²⁸, b¹¹r=ab¹⁰q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=ab⁶r, gr=b⁷r, hr=ab⁸r, ir=b⁹r, jr=ab¹⁰r, kr=ab¹⁰q, lr=b¹¹q, mr=b¹¹p, nr=ab¹²p, or=ab²⁷, pr=b²⁸, qr=ab²⁷, r²=b²⁸, b¹⁰s=ab⁹r, cs=ab²s, ds=ab⁴s, es=b⁵s, fs=ab⁶s, gs=b⁷s, hs=ab⁸s, is=b⁹s, js=b⁹r, ks=ab¹⁰r, ls=ab¹⁰q, ms=b¹¹q, ns=b¹¹p, os=ab¹²p, ps=ab²⁷, qs=b²⁸, rs=ab²⁷, s²=b²⁸, b⁹t=ab⁸s, ct=ab²t, dt=ab⁴t, et=b⁵t, ft=ab⁶t, gt=b⁷t, ht=ab⁸t, it=ab⁸s, jt=b⁹s, kt=b⁹r, lt=ab¹⁰r, mt=ab¹⁰q, nt=b¹¹q, ot=b¹¹p, pt=ab¹²p, qt=ab²⁷, rt=b²⁸, st=ab²⁷, t²=b²⁸, b⁸u=ab⁷t, cu=ab²u, du=ab⁴u, eu=b⁵u, fu=ab⁶u, gu=b⁷u, hu=b⁷t, iu=ab⁸t, ju=ab⁸s, ku=b⁹s, lu=b⁹r, mu=ab¹⁰r, nu=ab¹⁰q, ou=b¹¹q, pu=b¹¹p, qu=ab¹²p, ru=ab²⁷, su=b²⁸, tu=ab²⁷, u²=b²⁸, b⁷v=ab⁶u, cv=ab²v, dv=ab⁴v, ev=b⁵v, fv=ab⁶v, gv=ab⁶u, hv=b⁷u, iv=b⁷t, jv=ab⁸t, kv=ab⁸s, lv=b⁹s, mv=b⁹r, nv=ab¹⁰r, ov=ab¹⁰q, pv=b¹¹q, qv=b¹¹p, rv=ab¹²p, sv=ab²⁷, tv=b²⁸, uv=ab²⁷, v²=b²⁸, b⁶w=ab⁵v, cw=ab²w, dw=ab⁴w, ew=b⁵w, fw=b⁵v, gw=ab⁶v, hw=ab⁶u, iw=b⁷u, jw=b⁷t, kw=ab⁸t, lw=ab⁸s, mw=b⁹s, nw=b⁹r, ow=ab¹⁰r, pw=ab¹⁰q, qw=b¹¹q, rw=b¹¹p, sw=ab¹²p, tw=ab²⁷, uw=b²⁸, vw=ab²⁷, w²=b²⁸, b⁵x=ab⁴w, cx=ab²x, dx=ab⁴x, ex=ab⁴w, fx=b⁵w, gx=b⁵v, hx=ab⁶v, ix=ab⁶u, jx=b⁷u, kx=b⁷t, lx=ab⁸t, mx=ab⁸s, nx=b⁹s, ox=b⁹r, px=ab¹⁰r, qx=ab¹⁰q, rx=b¹¹q, sx=b¹¹p, tx=ab¹²p, ux=ab²⁷, vx=b²⁸, wx=ab²⁷, x²=b²⁸, b⁴y=ab³x, cy=ab²y, dy=b³x, ey=ab⁴x, fy=ab⁴w, gy=b⁵w, hy=b⁵v, iy=ab⁶v, jy=ab⁶u, ky=b⁷u, ly=b⁷t, my=ab⁸t, ny=ab⁸s, oy=b⁹s, py=b⁹r, qy=ab¹⁰r, ry=ab¹⁰q, sy=b¹¹q, ty=b¹¹p, uy=ab¹²p, vy=ab²⁷, wy=b²⁸, xy=ab²⁷, y²=b²⁸, b³z=ab²y, cz=ab²z, dz=b³y, ez=b³x, fz=ab⁴x, gz=ab⁴w, hz=b⁵w, iz=b⁵v, jz=ab⁶v, kz=ab⁶u, lz=b⁷u, mz=b⁷t, nz=ab⁸t, oz=ab⁸s, pz=b⁹s, qz=b⁹r, rz=ab¹⁰r, sz=ab¹⁰q, tz=b¹¹q, uz=b¹¹p, vz=ab¹²p, wz=ab²⁷, xz=b²⁸, yz=ab²⁷, z²=b²⁸, b²A=abz, cA=bz, dA=ab²y, eA=b³y, fA=b³x, gA=ab⁴x, hA=ab⁴w, iA=b⁵w, jA=b⁵v, kA=ab⁶v, lA=ab⁶u, mA=b⁷u, nA=b⁷t, oA=ab⁸t, pA=ab⁸s, qA=b⁹s, rA=b⁹r, sA=ab¹⁰r, tA=ab¹⁰q, uA=b¹¹q, vA=b¹¹p, wA=ab¹²p, xA=ab²⁷, yA=b²⁸, zA=ab²⁷, A²=b²⁸, b³B=aA, cB=ab²B, dB=bA, eB=bz, fB=ab²z, gB=ab²y, hB=b³y, iB=b³x, jB=ab⁴x, kB=ab⁴w, lB=b⁵w, mB=b⁵v, nB=ab⁶v, oB=ab⁶u, pB=b⁷u, qB=b⁷t, rB=ab⁸t, sB=ab⁸s, tB=b⁹s, uB=b⁹r, vB=ab¹⁰r, wB=ab¹⁰q, xB=b¹¹q, yB=b¹¹p, zB=ab¹²p, AB=ab²⁷, B²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, ae, bf, ag, ab²g, bh, b³h, ai, ab²i, ab⁴i, bj, b³j, b⁵j, ak, ab²k, ab⁴k, ab⁶k, bl, b³l, b⁵l, b⁷l, am, ab²m, ab⁴m, ab⁶m, ab⁸m, bn, b³n, b⁵n, b⁷n, b⁹n, ao, ab²o, ab⁴o, ab⁶o, ab⁸o, ab¹⁰o, bp, b³p, b⁵p, b⁷p, b⁹p, b¹¹p, aq, ab²q, ab⁴q, ab⁶q, ab⁸q, ab¹⁰q, br, b³r, b⁵r, b⁷r, b⁹r, as, ab²s, ab⁴s, ab⁶s, ab⁸s, bt, b³t, b⁵t, b⁷t, au, ab²u, ab⁴u, ab⁶u, bv, b³v, b⁵v, aw, ab²w, ab⁴w, bx, b³x, ay, ab²y, bz, aA, bB}

Phi = 1 a a a b b b a a c b b b³ c c d b³ b³ b⁵ d ab⁴ ab⁶ e b⁵ b⁷ f ab⁶ ab⁸ g b⁷ b⁹ h ab⁸ ab¹⁰ i b⁹ b¹¹ j ab¹⁰ ab¹² k b¹¹ b¹³ l ab¹² ab¹⁴ m b¹³ b¹⁵ n ab¹⁴ ab¹⁶ o b¹⁵ b¹⁷ p ab¹⁶ ab¹⁸ q b¹⁷ b¹⁹ r ab¹⁸ ab²⁰ s b¹⁹ b²¹ t ab²⁰ ab²² u b²¹ b²³ v ab²² ab²⁴ w b²³ b²⁵ x ab²⁴ ab²⁶ y b²⁵ b²⁷ z ab²⁶ ab²⁸ A b²⁷ b²⁷ b²B ab²⁸ ab²⁸ abB b²⁷ b²⁷ B ab²⁸ ab²⁸

Monoid Structure