Details Page for 0.1557

Complete Solution is Known:

MSV File: q-0.1557.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₂₁(0.1557):

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 | a²=1, b²⁷=b²⁵, 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=ab²⁵, n²=b²⁶, b¹²o=b²⁵, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁶o, go=b⁷o, ho=ab⁸o, io=b⁹o, jo=ab¹⁰o, ko=b¹¹o, lo=ab²⁵, mo=b²⁶, no=ab²⁵, o²=b²⁶, b¹¹p=ab¹⁰o, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁶p, gp=b⁷p, hp=ab⁸p, ip=b⁹p, jp=ab¹⁰p, kp=ab¹⁰o, lp=b¹¹o, mp=ab²⁵, np=b²⁶, op=ab²⁵, p²=b²⁶, b¹⁰q=ab⁹p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁶q, gq=b⁷q, hq=ab⁸q, iq=b⁹q, jq=b⁹p, kq=ab¹⁰p, lq=ab¹⁰o, mq=b¹¹o, nq=ab²⁵, oq=b²⁶, pq=ab²⁵, q²=b²⁶, b⁹r=ab⁸q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=ab⁶r, gr=b⁷r, hr=ab⁸r, ir=ab⁸q, jr=b⁹q, kr=b⁹p, lr=ab¹⁰p, mr=ab¹⁰o, nr=b¹¹o, or=ab²⁵, pr=b²⁶, qr=ab²⁵, r²=b²⁶, b⁸s=ab⁷r, cs=ab²s, ds=ab⁴s, es=b⁵s, fs=ab⁶s, gs=b⁷s, hs=b⁷r, is=ab⁸r, js=ab⁸q, ks=b⁹q, ls=b⁹p, ms=ab¹⁰p, ns=ab¹⁰o, os=b¹¹o, ps=ab²⁵, qs=b²⁶, rs=ab²⁵, s²=b²⁶, b⁷t=ab⁶s, ct=ab²t, dt=ab⁴t, et=b⁵t, ft=ab⁶t, gt=ab⁶s, ht=b⁷s, it=b⁷r, jt=ab⁸r, kt=ab⁸q, lt=b⁹q, mt=b⁹p, nt=ab¹⁰p, ot=ab¹⁰o, pt=b¹¹o, qt=ab²⁵, rt=b²⁶, st=ab²⁵, t²=b²⁶, b⁶u=ab⁵t, cu=ab²u, du=ab⁴u, eu=b⁵u, fu=b⁵t, gu=ab⁶t, hu=ab⁶s, iu=b⁷s, ju=b⁷r, ku=ab⁸r, lu=ab⁸q, mu=b⁹q, nu=b⁹p, ou=ab¹⁰p, pu=ab¹⁰o, qu=b¹¹o, ru=ab²⁵, su=b²⁶, tu=ab²⁵, u²=b²⁶, b⁵v=ab⁴u, cv=ab²v, dv=ab⁴v, ev=ab⁴u, fv=b⁵u, gv=b⁵t, hv=ab⁶t, iv=ab⁶s, jv=b⁷s, kv=b⁷r, lv=ab⁸r, mv=ab⁸q, nv=b⁹q, ov=b⁹p, pv=ab¹⁰p, qv=ab¹⁰o, rv=b¹¹o, sv=ab²⁵, tv=b²⁶, uv=ab²⁵, v²=b²⁶, b⁴w=ab³v, cw=ab²w, dw=b³v, ew=ab⁴v, fw=ab⁴u, gw=b⁵u, hw=b⁵t, iw=ab⁶t, jw=ab⁶s, kw=b⁷s, lw=b⁷r, mw=ab⁸r, nw=ab⁸q, ow=b⁹q, pw=b⁹p, qw=ab¹⁰p, rw=ab¹⁰o, sw=b¹¹o, tw=ab²⁵, uw=b²⁶, vw=ab²⁵, w²=b²⁶, b³x=ab²w, cx=ab²x, dx=b³w, ex=b³v, fx=ab⁴v, gx=ab⁴u, hx=b⁵u, ix=b⁵t, jx=ab⁶t, kx=ab⁶s, lx=b⁷s, mx=b⁷r, nx=ab⁸r, ox=ab⁸q, px=b⁹q, qx=b⁹p, rx=ab¹⁰p, sx=ab¹⁰o, tx=b¹¹o, ux=ab²⁵, vx=b²⁶, wx=ab²⁵, x²=b²⁶, b²y=abx, cy=bx, dy=ab²w, ey=b³w, fy=b³v, gy=ab⁴v, hy=ab⁴u, iy=b⁵u, jy=b⁵t, ky=ab⁶t, ly=ab⁶s, my=b⁷s, ny=b⁷r, oy=ab⁸r, py=ab⁸q, qy=b⁹q, ry=b⁹p, sy=ab¹⁰p, ty=ab¹⁰o, uy=b¹¹o, vy=ab²⁵, wy=b²⁶, xy=ab²⁵, y²=b²⁶, b³z=ay, cz=ab²z, dz=by, ez=bx, fz=ab²x, gz=ab²w, hz=b³w, iz=b³v, jz=ab⁴v, kz=ab⁴u, lz=b⁵u, mz=b⁵t, nz=ab⁶t, oz=ab⁶s, pz=b⁷s, qz=b⁷r, rz=ab⁸r, sz=ab⁸q, tz=b⁹q, uz=b⁹p, vz=ab¹⁰p, wz=ab¹⁰o, xz=b¹¹o, yz=ab²⁵, z²=b²⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, 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, aq, ab²q, ab⁴q, ab⁶q, ab⁸q, br, b³r, b⁵r, b⁷r, as, ab²s, ab⁴s, ab⁶s, bt, b³t, b⁵t, au, ab²u, ab⁴u, bv, b³v, aw, ab²w, bx, ay, bz}

Phi = 1 a a a a b b b b a a a c b b b b³ c c c d b³ b³ b³ b⁵ d d ab⁴ ab⁶ e e b⁵ b⁷ f f ab⁶ ab⁸ g g b⁷ b⁹ h h ab⁸ ab¹⁰ i i b⁹ b¹¹ j j ab¹⁰ ab¹² k k b¹¹ b¹³ l l ab¹² ab¹⁴ m m b¹³ b¹⁵ n n ab¹⁴ ab¹⁶ o o b¹⁵ b¹⁷ p p ab¹⁶ ab¹⁸ q q b¹⁷ b¹⁹ r r ab¹⁸ ab²⁰ s s b¹⁹ b²¹ t t ab²⁰ ab²² u u b²¹ b²³ v v ab²² ab²⁴ w w b²³ b²⁵ x x ab²⁴ ab²⁶ y y b²⁵ b²⁵ b²z b²z ab²⁶ ab²⁶ abz abz b²⁵ b²⁵ z z ab²⁶ ab²⁶

Monoid Structure