Details Page for 0.3072

Complete Solution is Known:

MSV File: q-0.3072.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₁₈(0.3072):

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, b²c=ab⁴, c²=b⁴, b²d=ab⁶, cd=b⁶, d²=b⁸, b²e=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b²f=ab⁷, ef=abdf, f²=b¹⁰, b²g=bcf, cg=abcf, dg=ab¹⁰, eg=b¹¹, fg=ab¹¹, g²=b¹², b³h=abdf, ch=ab²h, dh=b¹¹, eh=ab¹², fh=b¹², gh=ab¹³, h²=b¹⁴, b⁵i=b¹³, ci=ab²i, di=ab⁴i, ei=b¹³, fi=ab¹³, gi=b¹⁴, hi=ab¹⁵, i²=b¹⁶, b⁶j=ab¹⁵, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁵j, gj=ab¹⁵, hj=b¹⁶, ij=ab¹⁷, j²=b¹⁸, b⁷k=b¹⁷, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁵k, gk=b⁶k, hk=ab¹⁷, ik=b¹⁸, jk=ab¹⁹, k²=b²⁰, b⁸l=ab¹⁹, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁵l, gl=b⁶l, hl=ab⁷l, il=ab¹⁹, jl=b²⁰, kl=ab²¹, l²=b²², b⁹m=b²¹, cm=ab²m, dm=ab⁴m, em=b⁵m, fm=ab⁵m, gm=b⁶m, hm=ab⁷m, im=b⁸m, jm=ab²¹, km=b²², lm=ab²³, m²=b²⁴, b¹⁰n=ab²³, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁵n, gn=b⁶n, hn=ab⁷n, in=b⁸n, jn=ab⁹n, kn=ab²³, ln=b²⁴, mn=ab²⁵, n²=b²⁴, b¹¹o=b²⁵, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁵o, go=b⁶o, ho=ab⁷o, io=b⁸o, jo=ab⁹o, ko=b¹⁰o, lo=ab²⁵, mo=b²⁴, no=ab²⁵, o²=b²⁴, b¹¹p=ab¹⁰o, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁵p, gp=b⁶p, hp=ab⁷p, ip=b⁸p, jp=ab⁹p, kp=b¹⁰p, lp=b¹⁰o, mp=ab²⁵, np=b²⁴, op=ab²⁵, p²=b²⁴, b¹⁰q=ab⁹p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁵q, gq=b⁶q, hq=ab⁷q, iq=b⁸q, jq=ab⁹q, kq=ab⁹p, lq=b¹⁰p, mq=b¹⁰o, nq=ab²⁵, oq=b²⁴, pq=ab²⁵, q²=b²⁴, b⁹r=ab⁸q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=ab⁵r, gr=b⁶r, hr=ab⁷r, ir=b⁸r, jr=b⁸q, kr=ab⁹q, lr=ab⁹p, mr=b¹⁰p, nr=b¹⁰o, or=ab²⁵, pr=b²⁴, qr=ab²⁵, r²=b²⁴, b⁸s=ab⁷r, cs=ab²s, ds=ab⁴s, es=b⁵s, fs=ab⁵s, gs=b⁶s, hs=ab⁷s, is=ab⁷r, js=b⁸r, ks=b⁸q, ls=ab⁹q, ms=ab⁹p, ns=b¹⁰p, os=b¹⁰o, ps=ab²⁵, qs=b²⁴, rs=ab²⁵, s²=b²⁴, b⁷t=ab⁶s, ct=ab²t, dt=ab⁴t, et=b⁵t, ft=ab⁵t, gt=b⁶t, ht=b⁶s, it=ab⁷s, jt=ab⁷r, kt=b⁸r, lt=b⁸q, mt=ab⁹q, nt=ab⁹p, ot=b¹⁰p, pt=b¹⁰o, qt=ab²⁵, rt=b²⁴, st=ab²⁵, t²=b²⁴, b⁶u=ab⁵t, cu=ab²u, du=ab⁴u, eu=b⁵u, fu=ab⁵u, gu=ab⁵t, hu=b⁶t, iu=b⁶s, ju=ab⁷s, ku=ab⁷r, lu=b⁸r, mu=b⁸q, nu=ab⁹q, ou=ab⁹p, pu=b¹⁰p, qu=b¹⁰o, ru=ab²⁵, su=b²⁴, tu=ab²⁵, u²=b²⁴, b⁵v=ab⁴u, cv=ab²v, dv=ab⁴v, ev=ab⁴u, fv=b⁴u, gv=ab⁵u, hv=ab⁵t, iv=b⁶t, jv=b⁶s, kv=ab⁷s, lv=ab⁷r, mv=b⁸r, nv=b⁸q, ov=ab⁹q, pv=ab⁹p, qv=b¹⁰p, rv=b¹⁰o, sv=ab²⁵, tv=b²⁴, uv=ab²⁵, v²=b²⁴, b⁴w=ab³v, cw=ab²w, dw=b³v, ew=ab⁴v, fw=b⁴v, gw=b⁴u, hw=ab⁵u, iw=ab⁵t, jw=b⁶t, kw=b⁶s, lw=ab⁷s, mw=ab⁷r, nw=b⁸r, ow=b⁸q, pw=ab⁹q, qw=ab⁹p, rw=b¹⁰p, sw=b¹⁰o, tw=ab²⁵, uw=b²⁴, vw=ab²⁵, w²=b²⁴, b³x=ab²w, cx=ab²x, dx=b³w, ex=b³v, fx=ab³v, gx=b⁴v, hx=b⁴u, ix=ab⁵u, jx=ab⁵t, kx=b⁶t, lx=b⁶s, mx=ab⁷s, nx=ab⁷r, ox=b⁸r, px=b⁸q, qx=ab⁹q, rx=ab⁹p, sx=b¹⁰p, tx=b¹⁰o, ux=ab²⁵, vx=b²⁴, wx=ab²⁵, x²=b²⁴, b⁵y=bx, cy=ab²y, dy=ab⁴y, ey=bx, fy=abx, gy=b²x, hy=b²w, iy=ab³w, jy=ab³v, ky=b⁴v, ly=b⁴u, my=ab⁵u, ny=ab⁵t, oy=b⁶t, py=b⁶s, qy=ab⁷s, ry=ab⁷r, sy=b⁸r, ty=b⁸q, uy=ab⁹q, vy=ab⁹p, wy=b¹⁰p, xy=b¹⁰o, y²=b²⁴>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, ae, bf, abg, h, b²h, abi, ab³i, j, b²j, b⁴j, abk, ab³k, ab⁵k, l, b²l, b⁴l, b⁶l, abm, ab³m, ab⁵m, ab⁷m, n, b²n, b⁴n, b⁶n, b⁸n, abo, ab³o, ab⁵o, ab⁷o, ab⁹o, p, b²p, b⁴p, b⁶p, b⁸p, b¹⁰p, abq, ab³q, ab⁵q, ab⁷q, ab⁹q, r, b²r, b⁴r, b⁶r, b⁸r, abs, ab³s, ab⁵s, ab⁷s, t, b²t, b⁴t, b⁶t, abu, ab³u, ab⁵u, v, b²v, b⁴v, abw, ab³w, x, b²x, y, b²y, b⁴y}

Phi = 1 a 1 a 1 b ab b ab a 1 a 1 b ab b ab c ac c b² abc bc abc ab³ d ad d b⁴ e ae e f abe g abe b⁶ bg h bg ab⁷ bh i bh b⁸ bi j bi ab⁹ bj k bj b¹⁰ bk l bk ab¹¹ bl m bl b¹² bm n bm ab¹³ bn o bn b¹⁴ bo p bo ab¹⁵ bp q bp b¹⁶ bq r bq ab¹⁷ br s br b¹⁸ bs t bs ab¹⁹ bt u bt b²⁰ bu v bu ab²¹ bv w bv b²² bw x bw ab²³ bx ab³y bx b²⁴ ab⁴y b²y ab⁴y ab²⁵ b³y aby b³y b²⁴ ab²y y ab²y ab²⁵ by

Monoid Structure