Details Page for 0.1574

Complete Solution is Known:

MSV File: q-0.1574.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₉(0.1574):

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 | a²=1, b²⁶=b²⁴, 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=b²⁴, b¹¹n=ab²⁵, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁶n, gn=b⁷n, hn=ab⁸n, in=b⁹n, jn=ab¹⁰n, kn=ab²⁵, ln=b²⁴, mn=ab²⁵, n²=b²⁴, b¹¹o=ab¹⁰n, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁶o, go=b⁷o, ho=ab⁸o, io=b⁹o, jo=ab¹⁰o, ko=ab¹⁰n, lo=ab²⁵, mo=b²⁴, no=ab²⁵, o²=b²⁴, b¹⁰p=ab⁹o, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁶p, gp=b⁷p, hp=ab⁸p, ip=b⁹p, jp=b⁹o, kp=ab¹⁰o, lp=ab¹⁰n, mp=ab²⁵, np=b²⁴, op=ab²⁵, p²=b²⁴, b⁹q=ab⁸p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁶q, gq=b⁷q, hq=ab⁸q, iq=ab⁸p, jq=b⁹p, kq=b⁹o, lq=ab¹⁰o, mq=ab¹⁰n, nq=ab²⁵, oq=b²⁴, pq=ab²⁵, q²=b²⁴, b⁸r=ab⁷q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=ab⁶r, gr=b⁷r, hr=b⁷q, ir=ab⁸q, jr=ab⁸p, kr=b⁹p, lr=b⁹o, mr=ab¹⁰o, nr=ab¹⁰n, or=ab²⁵, pr=b²⁴, qr=ab²⁵, r²=b²⁴, b⁷s=ab⁶r, cs=ab²s, ds=ab⁴s, es=b⁵s, fs=ab⁶s, gs=ab⁶r, hs=b⁷r, is=b⁷q, js=ab⁸q, ks=ab⁸p, ls=b⁹p, ms=b⁹o, ns=ab¹⁰o, os=ab¹⁰n, ps=ab²⁵, qs=b²⁴, rs=ab²⁵, s²=b²⁴, b⁶t=ab⁵s, ct=ab²t, dt=ab⁴t, et=b⁵t, ft=b⁵s, gt=ab⁶s, ht=ab⁶r, it=b⁷r, jt=b⁷q, kt=ab⁸q, lt=ab⁸p, mt=b⁹p, nt=b⁹o, ot=ab¹⁰o, pt=ab¹⁰n, qt=ab²⁵, rt=b²⁴, st=ab²⁵, t²=b²⁴, b⁵u=ab⁴t, cu=ab²u, du=ab⁴u, eu=ab⁴t, fu=b⁵t, gu=b⁵s, hu=ab⁶s, iu=ab⁶r, ju=b⁷r, ku=b⁷q, lu=ab⁸q, mu=ab⁸p, nu=b⁹p, ou=b⁹o, pu=ab¹⁰o, qu=ab¹⁰n, ru=ab²⁵, su=b²⁴, tu=ab²⁵, u²=b²⁴, b⁴v=ab³u, cv=ab²v, dv=b³u, ev=ab⁴u, fv=ab⁴t, gv=b⁵t, hv=b⁵s, iv=ab⁶s, jv=ab⁶r, kv=b⁷r, lv=b⁷q, mv=ab⁸q, nv=ab⁸p, ov=b⁹p, pv=b⁹o, qv=ab¹⁰o, rv=ab¹⁰n, sv=ab²⁵, tv=b²⁴, uv=ab²⁵, v²=b²⁴, b³w=ab²v, cw=ab²w, dw=b³v, ew=b³u, fw=ab⁴u, gw=ab⁴t, hw=b⁵t, iw=b⁵s, jw=ab⁶s, kw=ab⁶r, lw=b⁷r, mw=b⁷q, nw=ab⁸q, ow=ab⁸p, pw=b⁹p, qw=b⁹o, rw=ab¹⁰o, sw=ab¹⁰n, tw=ab²⁵, uw=b²⁴, vw=ab²⁵, w²=b²⁴, b²x=abw, cx=bw, dx=ab²v, ex=b³v, fx=b³u, gx=ab⁴u, hx=ab⁴t, ix=b⁵t, jx=b⁵s, kx=ab⁶s, lx=ab⁶r, mx=b⁷r, nx=b⁷q, ox=ab⁸q, px=ab⁸p, qx=b⁹p, rx=b⁹o, sx=ab¹⁰o, tx=ab¹⁰n, ux=ab²⁵, vx=b²⁴, wx=ab²⁵, x²=b²⁴, by=ax, cy=bx, dy=ab²w, ey=ab²v, fy=b³v, gy=b³u, hy=ab⁴u, iy=ab⁴t, jy=b⁵t, ky=b⁵s, ly=ab⁶s, my=ab⁶r, ny=b⁷r, oy=b⁷q, py=ab⁸q, qy=ab⁸p, ry=b⁹p, sy=b⁹o, ty=ab¹⁰o, uy=ab¹⁰n, vy=ab²⁵, wy=b²⁴, xy=ab²⁵, y²=b²⁴, bz=ay, cz=ax, dz=bw, ez=ab²w, fz=ab²v, gz=b³v, hz=b³u, iz=ab⁴u, jz=ab⁴t, kz=b⁵t, lz=b⁵s, mz=ab⁶s, nz=ab⁶r, oz=b⁷r, pz=b⁷q, qz=ab⁸q, rz=ab⁸p, sz=b⁹p, tz=b⁹o, uz=ab¹⁰o, vz=ab¹⁰n, wz=ab²⁵, xz=b²⁴, yz=ab²⁵, z²=b²⁴, bA=az, cA=ay, dA=bx, eA=bw, fA=ab²w, gA=ab²v, hA=b³v, iA=b³u, jA=ab⁴u, kA=ab⁴t, lA=b⁵t, mA=b⁵s, nA=ab⁶s, oA=ab⁶r, pA=b⁷r, qA=b⁷q, rA=ab⁸q, sA=ab⁸p, tA=b⁹p, uA=b⁹o, vA=ab¹⁰o, wA=ab¹⁰n, xA=ab²⁵, yA=b²⁴, zA=ab²⁵, A²=b²⁴>

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

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

Monoid Structure