Details Page for 0.7132

Complete Solution is Known:

MSV File: q-0.7132.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₀₆(0.7132):

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 | a²=1, b²⁶=b²⁴, bc=ab³, c²=b⁴, b²d=b⁵, cd=ab⁵, d²=b⁶, b³e=b⁷, ce=ab²e, de=b⁷, e²=b⁸, b⁴f=b⁹, cf=ab²f, df=b³f, ef=b⁹, f²=b¹⁰, b⁵g=b¹¹, cg=ab²g, dg=b³g, eg=b⁴g, fg=b¹¹, g²=b¹², b⁶h=b¹³, ch=ab²h, dh=b³h, eh=b⁴h, fh=b⁵h, gh=b¹³, h²=b¹⁴, b⁷i=b¹⁵, ci=ab²i, di=b³i, ei=b⁴i, fi=b⁵i, gi=b⁶i, hi=b¹⁵, i²=b¹⁶, b⁸j=b¹⁷, cj=ab²j, dj=b³j, ej=b⁴j, fj=b⁵j, gj=b⁶j, hj=b⁷j, ij=b¹⁷, j²=b¹⁸, b⁹k=b¹⁹, ck=ab²k, dk=b³k, ek=b⁴k, fk=b⁵k, gk=b⁶k, hk=b⁷k, ik=b⁸k, jk=b¹⁹, k²=b²⁰, b¹⁰l=b²¹, cl=ab²l, dl=b³l, el=b⁴l, fl=b⁵l, gl=b⁶l, hl=b⁷l, il=b⁸l, jl=b⁹l, kl=b²¹, l²=b²², b¹¹m=b²³, cm=ab²m, dm=b³m, em=b⁴m, fm=b⁵m, gm=b⁶m, hm=b⁷m, im=b⁸m, jm=b⁹m, km=b¹⁰m, lm=b²³, m²=b²⁴, b¹²n=b²⁵, cn=ab²n, dn=b³n, en=b⁴n, fn=b⁵n, gn=b⁶n, hn=b⁷n, in=b⁸n, jn=b⁹n, kn=b¹⁰n, ln=b¹¹n, mn=b²⁵, n²=b²⁴, b¹²o=b¹¹n, co=ab²o, do=b³o, eo=b⁴o, fo=b⁵o, go=b⁶o, ho=b⁷o, io=b⁸o, jo=b⁹o, ko=b¹⁰o, lo=b¹¹o, mo=b¹¹n, no=b²⁵, o²=b²⁴, b¹¹p=b¹⁰o, cp=ab²p, dp=b³p, ep=b⁴p, fp=b⁵p, gp=b⁶p, hp=b⁷p, ip=b⁸p, jp=b⁹p, kp=b¹⁰p, lp=b¹⁰o, mp=b¹¹o, np=b¹¹n, op=b²⁵, p²=b²⁴, b¹⁰q=b⁹p, cq=ab²q, dq=b³q, eq=b⁴q, fq=b⁵q, gq=b⁶q, hq=b⁷q, iq=b⁸q, jq=b⁹q, kq=b⁹p, lq=b¹⁰p, mq=b¹⁰o, nq=b¹¹o, oq=b¹¹n, pq=b²⁵, q²=b²⁴, b⁹r=b⁸q, cr=ab²r, dr=b³r, er=b⁴r, fr=b⁵r, gr=b⁶r, hr=b⁷r, ir=b⁸r, jr=b⁸q, kr=b⁹q, lr=b⁹p, mr=b¹⁰p, nr=b¹⁰o, or=b¹¹o, pr=b¹¹n, qr=b²⁵, r²=b²⁴, b⁸s=b⁷r, cs=ab²s, ds=b³s, es=b⁴s, fs=b⁵s, gs=b⁶s, hs=b⁷s, is=b⁷r, js=b⁸r, ks=b⁸q, ls=b⁹q, ms=b⁹p, ns=b¹⁰p, os=b¹⁰o, ps=b¹¹o, qs=b¹¹n, rs=b²⁵, s²=b²⁴, b⁷t=b⁶s, ct=ab²t, dt=b³t, et=b⁴t, ft=b⁵t, gt=b⁶t, ht=b⁶s, it=b⁷s, jt=b⁷r, kt=b⁸r, lt=b⁸q, mt=b⁹q, nt=b⁹p, ot=b¹⁰p, pt=b¹⁰o, qt=b¹¹o, rt=b¹¹n, st=b²⁵, t²=b²⁴, b⁶u=b⁵t, cu=ab²u, du=b³u, eu=b⁴u, fu=b⁵u, gu=b⁵t, hu=b⁶t, iu=b⁶s, ju=b⁷s, ku=b⁷r, lu=b⁸r, mu=b⁸q, nu=b⁹q, ou=b⁹p, pu=b¹⁰p, qu=b¹⁰o, ru=b¹¹o, su=b¹¹n, tu=b²⁵, u²=b²⁴, b⁵v=b⁴u, cv=ab²v, dv=b³v, ev=b⁴v, fv=b⁴u, gv=b⁵u, hv=b⁵t, iv=b⁶t, jv=b⁶s, kv=b⁷s, lv=b⁷r, mv=b⁸r, nv=b⁸q, ov=b⁹q, pv=b⁹p, qv=b¹⁰p, rv=b¹⁰o, sv=b¹¹o, tv=b¹¹n, uv=b²⁵, v²=b²⁴, b⁴w=b³v, cw=ab²w, dw=b³w, ew=b³v, fw=b⁴v, gw=b⁴u, hw=b⁵u, iw=b⁵t, jw=b⁶t, kw=b⁶s, lw=b⁷s, mw=b⁷r, nw=b⁸r, ow=b⁸q, pw=b⁹q, qw=b⁹p, rw=b¹⁰p, sw=b¹⁰o, tw=b¹¹o, uw=b¹¹n, vw=b²⁵, w²=b²⁴, b³x=b²w, cx=ab²x, dx=b²w, ex=b³w, fx=b³v, gx=b⁴v, hx=b⁴u, ix=b⁵u, jx=b⁵t, kx=b⁶t, lx=b⁶s, mx=b⁷s, nx=b⁷r, ox=b⁸r, px=b⁸q, qx=b⁹q, rx=b⁹p, sx=b¹⁰p, tx=b¹⁰o, ux=b¹¹o, vx=b¹¹n, wx=b²⁵, x²=b²⁴, b³y=bx, cy=ab²y, dy=bx, ey=b²x, fy=b²w, gy=b³w, hy=b³v, iy=b⁴v, jy=b⁴u, ky=b⁵u, ly=b⁵t, my=b⁶t, ny=b⁶s, oy=b⁷s, py=b⁷r, qy=b⁸r, ry=b⁸q, sy=b⁹q, ty=b⁹p, uy=b¹⁰p, vy=b¹⁰o, wy=b¹¹o, xy=b¹¹n, y²=b²⁴>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, d, be, f, b²f, bg, b³g, h, b²h, b⁴h, bi, b³i, b⁵i, j, b²j, b⁴j, b⁶j, bk, b³k, b⁵k, b⁷k, l, b²l, b⁴l, b⁶l, b⁸l, bm, b³m, b⁵m, b⁷m, b⁹m, n, b²n, b⁴n, b⁶n, b⁸n, b¹⁰n, bo, b³o, b⁵o, b⁷o, b⁹o, b¹¹o, p, b²p, b⁴p, b⁶p, b⁸p, b¹⁰p, bq, b³q, b⁵q, b⁷q, b⁹q, r, b²r, b⁴r, b⁶r, b⁸r, bs, b³s, b⁵s, b⁷s, t, b²t, b⁴t, b⁶t, bu, b³u, b⁵u, v, b²v, b⁴v, bw, b³w, x, b²x, y, b²y}

Phi = 1 a b a 1 ab 1 ab b a b c 1 ab ac ab³ b c d abd b² ad e abe b³ ae f abf b⁴ af g abg b⁵ ag h abh b⁶ ah i abi b⁷ ai j abj b⁸ aj k abk b⁹ ak l abl b¹⁰ al m abm b¹¹ am n abn b¹² an o abo b¹³ ao p abp b¹⁴ ap q abq b¹⁵ aq r abr b¹⁶ ar s abs b¹⁷ as t abt b¹⁸ at u abu b¹⁹ au v abv b²⁰ av w abw b²¹ aw x abx b²² ax by ab²y b²³ aby y aby b²⁴ ay

Monoid Structure