Details Page for 0.0145

Complete Solution is Known:

MSV File: q-0.0145.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₂(0.0145):

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, b⁴=b², b³c=bc, b²c²=c², c⁴=ac³, b³d=bd, c³d=ac³, bd²=b³, cd²=c, d³=d, b³e=be, bce=abe, c²e=b²e, bde=abe, be²=abc³, e³=e, bf=be, cf=ce, df=de, e²f=f, f²=d²e², c³g=ac³, beg=abe, fg=d²eg, g²=ac³, b³h=bh, c²h=c³, d²h=h, beh=abe, fh=eh, dh²=ah², h³=ah², b²i=i, c²i=abc³, d²i=i, ei=be, fi=be, cdgi=acgi, cghi=acgi, i²=ac³, b²j=j, cj=ci, d²j=j, ej=be, fj=be, hj=hi, ij=ac³, j²=ac³, b²k=k, c²k=abc³, cdk=ack, d²k=k, ek=be, fk=be, gk=adgi, chk=ack, ik=ac³, jk=ac³, k²=ac³, b²l=l, c²l=abc³, d²l=l, el=be, fl=be, hl=hk, il=ac³, jl=ac³, kl=ac³, l²=ac³, b²m=m, cm=bc², d²m=m, em=abe, fm=abe, hm=abc³, im=c³, jm=c³, km=c³, lm=c³, m²=ac³, c²n²=c², ben²=be, bghn²=bgh, in²=i, jn²=j, kn²=k, ln²=l, mn²=m, bn³=bn, n⁴=n², b²co=co, c²o=c³, b²do=do, d²o=b²o, beo=abe, ceo=b²e, deo=b²e, fo=ab²e, go=ac³, b²ho=ho, cho=b²cgh, eho=b²e, h²o=b²gh², io=gj, jo=gj, ko=adgj, lo=gl, mo=abc³, n²o=o, bo²=abc³, co²=c³, do²=c³, e²o²=o², ho²=c³, o³=c³, b³p=bp, c²p=c³, d²p=p, bep=abe, fp=ep, bgp=abc³, e²gp=gp, bchp=acgl, ip=bc³, jp=bc³, kp=bc³, lp=bc³, mp=abc³, bn²p=bp, op=ac³, p²=ac³, b²q=q, cq=abcl, d²q=q, eq=ab²e, fq=ab²e, gq=b²hp, dhq=ahq, h²q=ahq, iq=bc³, jq=bc³, kq=bc³, lq=bc³, mq=abc³, n²q=q, oq=b²hp, pq=ac³, q²=ac³, b²r=r, c²r=abc³, d²r=r, er=be, fr=be, gr=bdhp, chr=chi, ir=ac³, jr=ac³, kr=ac³, lr=ac³, mr=c³, n²r=r, or=bdhp, pr=bc³, qr=bc³, r²=ac³, b²s=s, c³s=bc³, d²s=s, es=be, fs=be, hs=bc³, is=ac³, js=ac³, ks=ac³, ls=ac³, n³s=ns, os=bc³, ps=bc³, qs=bc³, rs=ac³, s²=ac³, b³t=bt, c²t=bc²ns, bet=ben, d²et=et, ft=et, deht=aeht, eh²t=aeht, cgit=cgin, h²it=h²in, jt=it, ckt=ckn, h²kt=h²kn, d²nt=nt, bhn²t=bht, b²ot=ot, eot=ab²en, hot=b²ght, o²t=ac³n, dghpt=aghpt, bh²pt=bh²np, gh²pt=aghpt, hqt=hnq, h²rt=h²nr, mst=c³n, nst=abc³, bt²=bh²nt, dt²=at², ht²=at², it²=h²i, kt²=h²k, lt²=h²k, mt²=bc³, ot²=b²gh²nt, qt²=ahq, rt²=h²r, st²=abc³, n²t³=n³t², t⁴=t², bu=abc³n, c²u=ac³n, d²u=u, e²u=u, fu=eu, dhu=ahu, h²u=ahu, iu=abc³n, ju=abc³n, ku=abc³n, lu=abc³n, mu=bc³n, nu=ac³, ou=c³n, pu=c³n, qu=c³n, ru=abc³n, su=abc³n, t²u=ahu, u²=ac³, bv=be, c²v=b²e, d²v=v, e²v=v, fv=ev, gv=ab²e, dhv=ahv, h²v=ahv, iv=be, jv=be, kv=be, lv=be, mv=abe, n³v=nv, ov=ab²e, qv=ab²e, rv=be, sv=be, dtv=atv, htv=atv, ntv=b²e, ptv=aeghu, t³v=tv, uv=b²en, v²=ac³, b²w=w, c²w=abc³, d²w=w, ew=be, fw=be, cdgw=acgw, dhw=ahw, cghw=acgw, h²w=ahw, iw=ac³, jw=ac³, kw=ac³, lw=ac³, mw=c³, n²w=w, ow=gw, pw=bc³, qw=bc³, rw=ac³, sw=ac³, tw=bhpt, uw=abc³n, vw=be, w²=ac³, b²x=x, c²x=ac³n, d²x=x, ex=b²en, fx=b²en, gx=c³n, dhx=ahx, h²x=ahx, ix=abc³n, jx=abc³n, kx=abc³n, lx=abc³n, mx=bc³n, nx=ac³, ox=c³n, px=c³n, qx=c³n, rx=abc³n, sx=abc³n, tx=ac³, ux=ac³, vx=b²en, wx=abc³n, x²=ac³, by=abe, c²y=ab²e, e²y=y, fy=d²ey, gy=b²e, dhy=ahy, h²y=ahy, iy=abe, jy=abe, ky=abe, ly=abe, my=be, n²y=y, oy=b²e, qy=b²e, ry=abe, sy=abe, ty=egn²t, uy=ab²en, vy=c³, wy=abe, xy=ab²en, y²=ac³, b²z=z, c²z=abc³, d²z=z, ez=be, fz=be, gz=bc³, dhz=ahz, h²z=ahz, iz=ac³, jz=ac³, kz=ac³, lz=ac³, mz=c³, nz=abc³n, oz=bc³, pz=bc³, qz=bc³, rz=ac³, sz=ac³, tz=abc³n, uz=abc³n, vz=be, wz=ac³, xz=abc³n, yz=abe, z²=ac³>

P = {a, b², ac, ab²c, c², ac³, ad, ab²d, cd, b²cd, ac²d, d², ae, ae², ace², ade², cde², d²e², bg, b³g, bcg, ac²g, bdg, bcdg, ce²g, de²g, acde²g, ad²e²g, ah, ab²h, ch, b²ch, dh, b²dh, acdh, ab²cdh, ae²h, ce²h, de²h, acde²h, gh, b²gh, abcgh, e²gh, ace²gh, ade²gh, cde²gh, h², b²h², ach², ab²ch², e²h², ace²h², agh², ab²gh², bcgh², ae²gh², ce²gh², bi, bcdi, abhi, bdhi, abcdhi, abdghi, bh²i, bj, bdgj, bk, abck, abdk, abhk, bdhk, bh²k, bl, abcl, abdl, bcdl, abgl, abcdgl, abm, bdm, abdgm, n, bcn, bdn, e²n, efn, agn, b³gn, abcgn, abdgn, bcdgn, ae²gn, abchn, abghn, bcghn, abcdghn, bch²n, bgh²n, abcgh²n, an², b²n², acn², ab²cn², adn², ab²dn², cdn², b²cdn², d²n², aen², ae²n², ace²n², ade²n², cde²n², d²e²n², bgn², b³gn², bcgn², bdgn², bcdgn², ce²gn², de²gn², acde²gn², ad²e²gn², ahn², ab²hn², chn², b²chn², dhn², b²dhn², acdhn², ab²cdhn², ae²hn², ce²hn², de²hn², acde²hn², ghn², e²ghn², ace²ghn², ade²ghn², cde²ghn², h²n², b²h²n², ach²n², ab²ch²n², e²h²n², ace²h²n², agh²n², ae²gh²n², ce²gh²n², n³, e²n³, efn³, agn³, ae²gn³, ab²o, bco, e²o, ho, adho, ano, b³no, abcno, bcdno, ae²no, abhno, no², ap, ab²p, acdp, ab²cdp, acep, adep, ae²p, acde²p, gp, cdgp, hp, b²hp, adhp, ab²dhp, cdhp, cehp, e²hp, ade²hp, cde²hp, aghp, dghp, acdghp, ah²p, ab²h²p, aceh²p, ae²h²p, gh²p, cnp, dnp, ce²np, de²np, acgnp, adgnp, achnp, ace²hnp, cghnp, acgh²np, an²p, acdn²p, aden²p, ae²n²p, acde²n²p, gn²p, cdgn²p, hn²p, adhn²p, cdhn²p, e²hn²p, ade²hn²p, cde²hn²p, aghn²p, dghn²p, acdghn²p, ah²n²p, ae²h²n²p, ce²h²n²p, gh²n²p, cn³p, dn³p, ce²n³p, de²n³p, acgn³p, adgn³p, achn³p, ace²hn³p, cghn³p, acgh²n³p, aq, dq, hq, br, abdr, bcdr, abhr, bdhr, bh²r, bs, abcs, bc²s, abds, bcds, abc²ds, gs, abc²gs, cdgs, ams, dms, adgms, bn²s, abcn²s, abdn²s, bcdn²s, gn²s, cdgn²s, gt, nt, b²nt, acnt, ab²cnt, adnt, ab²dnt, cdnt, b²cdnt, e²nt, ace²nt, ade²nt, cde²nt, agnt, ab²gnt, bcgnt, bcdgnt, ae²gnt, ce²gnt, de²gnt, acde²gnt, ahnt, ab²hnt, chnt, b²chnt, dhnt, b²dhnt, acdhnt, ab²cdhnt, ae²hnt, ce²hnt, ghnt, b²ghnt, abcghnt, adghnt, ab²dghnt, e²ghnt, ace²ghnt, h²nt, b²h²nt, ach²nt, ab²ch²nt, agh²nt, ab²gh²nt, bcgh²nt, bint, abdint, bcdint, bdgint, abhint, bdhint, abcdhint, abdghint, bknt, abdknt, abhknt, bdhknt, blnt, abclnt, abdlnt, bcdlnt, abglnt, abcdglnt, abmnt, bdmnt, bgmnt, abdgmnt, n³t, acn³t, adn³t, cdn³t, e²n³t, ace²n³t, ade²n³t, cde²n³t, agn³t, ae²gn³t, ce²gn³t, de²gn³t, acde²gn³t, ahn³t, chn³t, dhn³t, acdhn³t, ae²hn³t, ce²hn³t, ghn³t, adghn³t, e²ghn³t, ace²ghn³t, h²n³t, ach²n³t, agh²n³t, anot, bcnot, dnot, cdept, cehpt, anpt, ab²npt, b²dnpt, acdnpt, ab²cdnpt, acenpt, adenpt, ae²npt, acde²npt, gnpt, cdgnpt, b²hnpt, ab²dhnpt, aehnpt, cghnpt, an³pt, dn³pt, acdn³pt, acen³pt, ae²n³pt, de²n³pt, acde²n³pt, gn³pt, adgn³pt, cdgn³pt, hn³pt, adhn³pt, e²hn³pt, aghn³pt, cghn³pt, ah²n³pt, anqt, dnqt, bnrt, abdnrt, bcdnrt, abhnrt, bdhnrt, bgst, bcdgst, t², act², e²t², ace²t², agt², ae²gt², ce²gt², n²t², acn²t², e²n²t², ace²n²t², agn²t², ae²gn²t², ce²gn²t², apt², acept², ae²pt², gpt², an²pt², acen²pt², ae²n²pt², gn²pt², nt³, acnt³, e²nt³, ace²nt³, agnt³, ae²gnt³, ce²gnt³, acept³, enpt³, acgnpt³, tu, actu, adtu, acdetu, agtu, cgtu, dgtu, ahtu, acehtu, ghtu, ev, acev, adev, cdev, aehv, cehv, en²v, acen²v, aden²v, cden²v, aehn²v, cehn²v, aepv, cepv, depv, ehpv, acdenpv, acehnpv, aen²pv, cen²pv, den²pv, ehn²pv, et²v, acet²v, bw, abdw, bcdw, bdgw, abhw, bcx, abchx, cey, dey, acdey, ad²ey, ehy, acehy, aeny, epy, acepy, cdepy, aehpy, cehpy, adenpy, bz, abdz, bcdz, abhz}

Phi = 1 1 a 1 a a be be be be abe b b a a c d e f abe be be be be g d²e²g c³ h b²e b²e b²e egh i j k l m n o b²p p q ab²e aegh abe abe abe r abc³ c³ s t ab²e b²e b²e abe ben ben be be c³ c³ u ac³n b²e b²e b²e v w bhp abc³ abc³ bc³ x ac³n ac³n ac³n y y ben ben ben z abc³ abc³ abc³

Monoid Structure