Details Page for 0.7135

Complete Solution is Known:

MSV File: q-0.7135.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₄₂(0.7135):

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,C,D,E | a²=1, b³=b, b²c=c, c¹¹=ac¹⁰, bd=ab, cd=ac, d²=b², b²e=e, c²e=abc³, de=ae, ce²=c³, e⁹=bc¹⁰, b²f=f, cf=abce, df=af, e⁸f=ac¹⁰, ef²=abe²f, f⁹=ac¹⁰, b²g=g, c²g=ac⁴, dg=ag, ceg=bc⁴, e⁷g=abc¹⁰, e⁶fg=c¹⁰, f³g=e²fg, cg²=c⁵, e²g²=ae⁴g, fg²=ae²fg, g³=e⁴g, b²h=h, ch=abcg, dh=ah, e²h=ae³f, f²h=bf⁴, fgh=be²fg, g²h=e³fg, h²=f⁴, b²i=i, ci=cg, di=ai, e³i=e³g, efi=efg, f²i=abefg, egi=eg², fgi=egh, ehi=ae²fg, fhi=abegh, ei²=ae³g, fi²=egh, gi²=g²i, hi²=e³fg, i³=e⁴g, b²j=j, c²j=abc⁵, dj=aj, cej=c⁵, e²j=ae³g, efj=egh, f²j=be²fg, cgj=bc⁶, egj=g²i, fgj=e³fg, g²j=ae⁵g, hj=e²fg, eij=e⁴g, fij=ghi, i²j=ae⁵g, j²=ae⁴g, b²k=k, ck=abcj, dk=ak, e²k=e⁴f, f²k=f⁵, egk=ghi, fgk=abe³fg, g²k=ae⁴fg, hk=bf⁵, eik=e³fg, fik=abghi, i²k=ae⁴fg, jk=ae³fg, k²=f⁶, b²l=l, c²l=ac⁶, dl=al, el=ij, fl=gk, cgl=c⁷, g²l=e⁶g, hl=ae³fg, i²l=e⁶g, jl=e⁵g, kl=e⁴fg, l²=ae⁶g, b²m=m, c³m=bc⁷, dm=am, cem=abc²m, e²m=ae⁵f, f²m=bf⁶, cgm=abc⁷, egm=gik, fgm=be⁴fg, g²m=e⁵fg, hm=f⁶, eim=ae⁴fg, fim=abgik, i²m=e⁵fg, jm=e⁴fg, km=bf⁷, lm=ae⁵fg, m²=f⁸, b²n=n, cn=abcm, dn=an, e²n=e⁴g, efn=ghi, f²n=abe³fg, gn=gl, hn=ae³fg, in=il, jn=e⁵g, kn=e⁴fg, ln=ae⁶g, mn=ae⁵fg, n²=ae⁶g, b²o=o, c³o=abc⁸, do=ao, ceo=abc²o, e²o=ae⁵g, efo=gik, f²o=be⁴fg, cgo=bc⁸, ego=gil, fgo=e⁵fg, g²o=bc¹⁰, ho=e⁴fg, eio=e⁶g, fio=gim, i²o=bc¹⁰, jo=ae⁶g, ko=ae⁵fg, lo=abc¹⁰, mo=c¹⁰, no=abc¹⁰, o²=c¹⁰, b²p=p, c⁴p=c⁹, dp=ap, cep=abc²p, e³p=e⁷f, efp=abe²p, f³p=f⁸, cgp=ac³p, egp=e⁵fg, fgp=abe⁵fg, g²p=ac¹⁰, hp=bf²p, ip=gp, jp=ae⁵fg, kp=f⁸, lp=c¹⁰, mp=abc¹⁰, np=c¹⁰, op=abc¹⁰, p²=c¹⁰, b²q=q, cq=abcp, dq=aq, e³q=ae⁶g, efq=agp, f³q=ae⁵fg, gq=ae²q, hq=bf²q, iq=ae²q, jq=ae⁶g, kq=ae⁵fg, lq=abc¹⁰, mq=c¹⁰, nq=abc¹⁰, oq=c¹⁰, pq=abc¹⁰, q²=c¹⁰, b²r=r, c⁴r=ac¹⁰, dr=ar, cer=abc²r, e³r=abc¹⁰, e²fr=bgio, f³r=c¹⁰, gr=ae²r, ehr=abgio, fhr=bc¹⁰, ir=ae²r, jr=abc¹⁰, kr=c¹⁰, lr=c¹⁰, mr=abc¹⁰, nr=c¹⁰, or=abc¹⁰, pr=c¹⁰, qr=abc¹⁰, r²=c¹⁰, b²s=s, c⁴s=gio, ds=as, ces=abc²s, e⁴s=bc¹⁰, efs=abe²s, f³s=abe³s, cgs=ac³s, e²gs=abc¹⁰, fgs=abegs, g²s=bc¹⁰, hs=bf²s, is=gs, js=aegs, ks=abe³s, ls=abc¹⁰, ms=c¹⁰, ns=abc¹⁰, os=c¹⁰, ps=abc¹⁰, qs=c¹⁰, rs=abc¹⁰, s²=c¹⁰, b²t=t, ct=abcs, dt=at, e³t=begs, eft=ags, f³t=e³s, gt=ae²t, ht=bf²t, it=ae²t, jt=begs, kt=e³s, lt=c¹⁰, mt=abc¹⁰, nt=c¹⁰, ot=abc¹⁰, pt=c¹⁰, qt=abc¹⁰, rt=c¹⁰, st=abc¹⁰, t²=c¹⁰, b²u=u, c⁴u=gio, du=au, ceu=abc²u, e⁴u=bc¹⁰, e²fu=c³u, f⁴u=bc¹⁰, gu=ae²u, ehu=ac³u, fhu=bf³u, iu=ae²u, ju=e³u, eku=abgio, fku=bc¹⁰, lu=abc¹⁰, mu=c¹⁰, nu=abc¹⁰, ou=c¹⁰, pu=abc¹⁰, qu=c¹⁰, ru=abc¹⁰, su=c¹⁰, tu=abc¹⁰, u²=c¹⁰, b²v=v, c³v=aefu, dv=av, cev=abc²v, e⁴v=ae³s, efv=abe²v, f²v=e²v, cgv=efu, e²gv=aegs, fgv=abegv, g²v=egs, hv=be²v, iv=gv, jv=aegv, kv=abe³v, lv=aegs, mv=abe³s, nv=aegs, ov=abc¹⁰, pv=c¹⁰, qv=abc¹⁰, rv=c¹⁰, sv=abc¹⁰, tv=c¹⁰, uv=abc¹⁰, v²=c¹⁰, b²w=w, cw=abcv, dw=aw, e²w=bgv, efw=agv, f⁴w=be³s, gw=abgv, hw=bf²w, iw=abgv, jw=begv, kw=f³w, lw=begs, mw=e³s, nw=begs, ow=c¹⁰, pw=abc¹⁰, qw=c¹⁰, rw=abc¹⁰, sw=c¹⁰, tw=abc¹⁰, uw=c¹⁰, vw=abc¹⁰, w²=c¹⁰, b²x=x, c³x=aefu, dx=ax, cex=abc²x, e³x=ae²u, efx=abc²x, f³x=bf²u, gx=ae²x, hx=bf²x, ix=ae²x, jx=ae²u, kx=hu, lx=e³u, mx=ku, nx=e³u, ox=abc¹⁰, px=c¹⁰, qx=abc¹⁰, rx=c¹⁰, sx=abc¹⁰, tx=c¹⁰, ux=abc¹⁰, vx=c¹⁰, wx=abc¹⁰, x²=c¹⁰, b²y=y, c³y=bc²x, dy=ay, cey=abc²y, e³y=ae²v, fy=abey, cgy=abc²x, egy=agv, g²y=egv, hy=be²y, iy=gy, jy=gv, ky=be²v, ly=aegv, my=abe³v, ny=aegv, oy=aegs, py=abe³s, qy=aegs, ry=abc¹⁰, sy=c¹⁰, ty=abc¹⁰, uy=c¹⁰, vy=abc¹⁰, wy=c¹⁰, xy=abc¹⁰, y²=c¹⁰, b²z=z, cz=abcy, dz=az, e²z=bgy, efz=agy, f³z=bf²w, gz=abgy, hz=bf²z, iz=abgy, jz=abgv, kz=bf²w, lz=begv, mz=f³w, nz=begv, oz=begs, pz=e³s, qz=begs, rz=c¹⁰, sz=abc¹⁰, tz=c¹⁰, uz=abc¹⁰, vz=c¹⁰, wz=abc¹⁰, xz=c¹⁰, yz=abc¹⁰, z²=c¹⁰, b²A=A, c²A=c²y, dA=aA, ceA=abc²y, e²A=aex, efA=abc²y, f²A=bfx, gA=ex, hA=fx, iA=ex, jA=ae²x, kA=bf²x, lA=ae²u, mA=hu, nA=ae²u, oA=e³u, pA=ku, qA=e³u, rA=abc¹⁰, sA=c¹⁰, tA=abc¹⁰, uA=c¹⁰, vA=abc¹⁰, wA=c¹⁰, xA=abc¹⁰, yA=c¹⁰, zA=abc¹⁰, A²=c¹⁰, b²B=B, c²B=bcA, dB=aB, ceB=acA, e²B=aeA, efB=acA, f²B=bfA, gB=eA, hB=fA, iB=eA, jB=ex, kB=fx, lB=ae²x, mB=bf²x, nB=ae²x, oB=ae²u, pB=hu, qB=ae²u, rB=e³u, sB=ku, tB=e³u, uB=abc¹⁰, vB=c¹⁰, wB=abc¹⁰, xB=c¹⁰, yB=abc¹⁰, zB=c¹⁰, AB=abc¹⁰, B²=c¹⁰, b²C=C, c²C=bcB, dC=aC, ceC=acB, e²C=aeB, efC=acB, f²C=bfB, gC=eB, hC=fB, iC=eB, jC=eA, kC=fA, lC=ex, mC=fx, nC=ex, oC=ae²x, pC=bf²x, qC=ae²x, rC=ae²u, sC=hu, tC=ae²u, uC=e³u, vC=ku, wC=e³u, xC=abc¹⁰, yC=c¹⁰, zC=abc¹⁰, AC=c¹⁰, BC=abc¹⁰, C²=c¹⁰, b²D=D, c²D=bcC, dD=aD, ceD=acC, e⁴D=aey, fD=abeD, cgD=acB, e²gD=abez, g²D=bez, hD=be²D, iD=gD, jD=aegD, kD=abe³D, lD=abez, mD=abey, nD=abez, oD=gy, pD=be²y, qD=gy, rD=gv, sD=be²v, tD=gv, uD=aegv, vD=abe³v, wD=aegv, xD=aegs, yD=abe³s, zD=aegs, AD=abc¹⁰, BD=c¹⁰, CD=abc¹⁰, D²=c¹⁰, b²E=E, cE=abcD, dE=aE, e²E=bgD, efE=agD, f⁴E=bfz, gE=abgD, hE=bf²E, iE=abgD, jE=begD, kE=f³E, lE=ez, mE=fz, nE=ez, oE=abgy, pE=bf²z, qE=abgy, rE=abgv, sE=bf²w, tE=abgv, uE=begv, vE=f³w, wE=begv, xE=begs, yE=e³s, zE=begs, AE=c¹⁰, BE=abc¹⁰, CE=c¹⁰, DE=abc¹⁰, E²=c¹⁰>

P = {a, b², abc, c², ac³, c⁴, ac⁵, c⁶, ac⁷, c⁸, ac⁹, c¹⁰, e², be³, e⁴, be⁵, e⁶, be⁷, e⁸, aef, abe³f, ae⁴f, abe⁵f, ae⁶f, abe⁷f, f², af³, f⁴, af⁵, f⁶, af⁷, f⁸, aeg, abe³g, ae⁴g, abe⁵g, ae⁶g, fg, e²fg, be³fg, e⁴fg, be⁵fg, af²g, g², bh, eh, abfh, abgh, abei, ae²i, bfi, bgi, abhi, i², aj, bl, am, cm, bn, co, bp, abcp, bc²p, ae²p, af²p, abeq, bf²q, br, abcr, bc²r, er, aefr, abhr, cs, ac²s, c³s, abes, e³s, fs, gs, et, be²t, abft, au, cu, ac²u, c³u, abeu, ae²u, fu, befu, af²u, abku, abcv, bc²v, ev, be²v, abfv, abgv, aegv, aw, abew, fw, af²w, bx, abcx, bc²x, ex, be²x, abfx, bf²x, ay, cy, ac²y, abey, ae²y, gy, bz, ez, abfz, bf²z, aA, cA, abeA, fA, bB, abcB, eB, abfB, aC, cC, abeC, fC, bD, abcD, eD, be²D, e³D, abgD, aegD, aE, abeE, fE, af²E, f³E}

Phi = 1 a b a b c b d b ab² e f e g h i j k j l m n o p q r s t u v w x y z A e²D f²E B aeD bfE C D E

Monoid Structure