Details Page for 0.7165

Complete Solution is Known:

MSV File: q-0.7165.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₄(0.7165):

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 | a²=1, b³=b, b²c=c, c⁸=ac⁷, bd=ab, cd=ac, d²=b², b²e=e, c²e=abc³, de=ae, ce²=c³, e⁶=ac⁷, b²f=f, cf=abce, df=af, e³f=abe⁴, ef²=abe²f, f⁵=abe⁵, b²g=g, c²g=ac⁴, dg=ag, ceg=bc⁴, e⁴g=c⁷, efg=abe²g, f³g=abe³g, cg²=c⁵, e²g²=ac⁷, fg²=be³g, g³=c⁷, b²h=h, ch=abcg, dh=ah, e²h=be⁴, f²h=bf⁴, gh=abg², h²=f⁴, b²i=i, ci=cg, di=ai, e²i=f²g, fi=abeg, egi=eg², ehi=be³g, i²=abhi, b²j=j, c²j=abc⁵, dj=aj, cej=c⁵, e³j=ac⁷, e²fj=bc⁷, f²j=e²j, cgj=bc⁶, egj=g²i, fgj=abc⁷, g²j=abc⁷, ehj=abc⁷, fhj=c⁷, eij=c⁷, gij=abg²i, hij=c⁷, cj²=c⁷, ej²=abc⁷, fj²=c⁷, gj²=c⁷, hj²=abc⁷, ij²=c⁷, j³=abc⁷, b²k=k, ck=abcj, dk=ak, e³k=bc⁷, e²fk=ac⁷, f²k=e²k, egk=abg²i, fgk=c⁷, g²k=c⁷, ehk=c⁷, fhk=abc⁷, eik=abc⁷, gik=g²i, hik=abc⁷, ejk=g²i, fjk=abg²i, gjk=abg²i, hjk=g²i, ijk=abg²i, j²k=g²i, ek²=abc⁷, fk²=c⁷, gk²=c⁷, hk²=abc⁷, ik²=c⁷, jk²=abg²i, k³=c⁷, b²l=l, cl=cj, dl=al, e²l=ae³g, efl=abeg², f²l=ae³g, egl=g²i, fgl=abc⁷, g²l=abc⁷, hl=abe³g, eil=c⁷, gil=abg²i, jl=j², kl=abk², l²=ac⁷, b²m=m, c²m=ac⁶, dm=am, cem=bc⁶, e²m=c⁷, efm=abg²i, f²m=c⁷, cgm=c⁷, egm=abg²i, fgm=c⁷, g²m=c⁷, hm=bc⁷, eim=abc⁷, gim=g²i, jm=abj², km=k², lm=bc⁷, m²=ac⁷, b²n=n, cn=abcm, dn=an, e²n=abc⁷, efn=g²i, f²n=abc⁷, gn=abgm, hn=ac⁷, in=abim, jn=j², kn=abk², ln=ac⁷, mn=bc⁷, n²=ac⁷, b²o=o, co=cm, do=ao, eo=il, fo=abgl, go=gm, ho=bc⁷, io=im, jo=abj², k²o=c⁷, lo=bc⁷, mo=ac⁷, no=bc⁷, o²=ac⁷, b²p=p, c²p=abg²i, dp=ap, cep=g²i, e²p=abc⁷, efp=g²i, f²p=abc⁷, gp=abgm, hp=ac⁷, ip=abim, cjp=c⁷, ejp=abc⁷, fjp=c⁷, j²p=abc⁷, kp=abko, lp=ac⁷, mp=bc⁷, np=ac⁷, op=bc⁷, p²=ac⁷, b²q=q, cq=abcp, dq=aq, e²q=c⁷, fq=abeq, gq=ag²i, hq=bc⁷, iq=ag²i, jq=bg²i, kq=ag²i, lq=bc⁷, mq=ac⁷, nq=bc⁷, oq=ac⁷, pq=bc⁷, q²=ac⁷, b²r=r, cr=cp, dr=ar, er=abeq, fr=eq, gr=bg²i, hr=ac⁷, ir=bg²i, jr=ag²i, kr=bg²i, lr=ac⁷, mr=bc⁷, nr=ac⁷, or=bc⁷, pr=ac⁷, qr=bc⁷, r²=ac⁷, b²s=s, c³s=ag²i, ds=as, ces=abc²s, e³s=bc⁷, fs=abes, gs=abeq, hs=be²s, is=abeq, js=bg²i, ks=ac⁷, ls=bc⁷, ms=ac⁷, ns=bc⁷, os=ac⁷, ps=bc⁷, qs=ac⁷, rs=bc⁷, s²=ac⁷, b²t=t, ct=abcs, dt=at, e²t=aeq, eft=beq, f²t=abe²s, gt=eq, ht=ae²s, it=eq, jt=ac⁷, kt=bg²i, lt=ac⁷, mt=bc⁷, nt=ac⁷, ot=bc⁷, pt=ac⁷, qt=bc⁷, rt=ac⁷, st=bc⁷, t²=ac⁷, b²u=u, cu=cs, du=au, eu=abet, fu=abft, gu=abeq, hu=be²s, iu=abeq, ju=bg²i, ku=ag²i, lu=bc⁷, mu=ac⁷, nu=bc⁷, ou=ac⁷, pu=bc⁷, qu=ac⁷, ru=bc⁷, su=ac⁷, tu=bc⁷, u²=ac⁷, b²v=v, c²v=bcs, dv=av, cev=acs, e²v=aes, fv=abev, gv=abet, hv=abes, iv=abet, jv=abeq, kv=eq, lv=abeq, mv=bc⁷, nv=ac⁷, ov=bc⁷, pv=ac⁷, qv=bc⁷, rv=ac⁷, sv=bc⁷, tv=ac⁷, uv=bc⁷, v²=ac⁷, b²w=w, cw=abcv, dw=aw, e²w=aet, efw=bet, f²w=bft, gw=et, hw=ft, iw=et, jw=eq, kw=ac²s, lw=eq, mw=ac⁷, nw=bg²i, ow=ac⁷, pw=bc⁷, qw=ac⁷, rw=bc⁷, sw=ac⁷, tw=bc⁷, uw=ac⁷, vw=bc⁷, w²=ac⁷, b²x=x, cx=cv, dx=ax, e²x=bet, efx=aet, f²x=aft, gx=abet, hx=abft, ix=abet, jx=ac²s, kx=bc²s, lx=abeq, mx=bg²i, nx=ag²i, ox=bc⁷, px=ac⁷, qx=bc⁷, rx=ac⁷, sx=bc⁷, tx=ac⁷, ux=bc⁷, vx=ac⁷, wx=bc⁷, x²=ac⁷, b²y=y, c²y=bcv, dy=ay, cey=acv, e²y=aev, fy=abey, cgy=acs, egy=bet, g²y=beq, hy=abev, iy=gy, jy=abet, ky=et, ly=abet, my=abeq, ny=eq, oy=abeq, py=bc⁷, qy=ac⁷, ry=bc⁷, sy=ac⁷, ty=bc⁷, uy=ac⁷, vy=bc⁷, wy=ac⁷, xy=bc⁷, y²=ac⁷, b²z=z, cz=abcy, dz=az, e²z=aew, efz=bew, f²z=bfw, gz=ew, hz=fw, iz=ew, jz=et, kz=abcs, lz=et, mz=eq, nz=ac²s, oz=eq, pz=ac⁷, qz=bg²i, rz=ac⁷, sz=bc⁷, tz=ac⁷, uz=bc⁷, vz=ac⁷, wz=bc⁷, xz=ac⁷, yz=bc⁷, z²=ac⁷, b²A=A, cA=cy, dA=aA, e²A=aex, fA=bx, gA=ex, hA=fx, iA=ex, jA=abcs, kA=cs, lA=abet, mA=ac²s, nA=bc²s, oA=abeq, pA=bg²i, qA=ag²i, rA=bc⁷, sA=ac⁷, tA=bc⁷, uA=ac⁷, vA=bc⁷, wA=ac⁷, xA=bc⁷, yA=ac⁷, zA=bc⁷, A²=ac⁷, b²B=B, c²B=bcy, dB=aB, ceB=acy, e²B=aey, fB=abeB, cgB=acv, egB=agy, g²B=bet, hB=abey, iB=gB, jB=gy, kB=abgy, lB=gy, mB=abet, nB=et, oB=abet, pB=abeq, qB=eq, rB=abeq, sB=bc⁷, tB=ac⁷, uB=bc⁷, vB=ac⁷, wB=bc⁷, xB=ac⁷, yB=bc⁷, zB=ac⁷, AB=bc⁷, B²=ac⁷>

P = {a, b², abc, c², ac³, c⁴, ac⁵, c⁶, ac⁷, e², be³, e⁴, be⁵, aef, f², af³, f⁴, aeg, abe³g, fg, af²g, g², bh, eh, abfh, abei, bgi, abhi, be²j, hj, j², ae²k, abhk, ajk, k², al, bm, an, bo, cp, bq, bs, abcs, bc²s, ae²s, abet, cv, abev, ew, abfw, ax, abex, fx, abcy, ey, abgy, az, abez, fz, bA, eA, cB, abeB, gB}

Phi = 1 a b a b c b d b d e f e g h i j k l m n o p q r s t u v w x y z A B

Monoid Structure