Details Page for 0.35

Complete Solution is Known:

MSV File: q-0.35.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₀(0.35):

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 | a²=1, b³=b, b²c=c, c⁴=c³, b²d=d, c³d=c²d, cd²=d², d³=ad², b²e=e, c³e=bc³, c²de=bc²d, d²e=bd², c²e²=c², ce³=ce, e⁴=e², b²f=f, cdf=df, d²f=ad², def=bdf, c²f²=d², df²=ad², e²f²=f², f³=acf², b²g=g, c²g=bc³, cdg=bc²d, d²g=bd², dfg=bdf, ce²fg=cfg, f²g=cef², eg²=bcg², cfg²=c³f, cg³=bc³, dg³=bdg², fg³=bfg², g⁸=bg⁷, b²h=h, ch=c², d²h=d², deh=cde, e³h=eh, fh=cf, gh=cg, dh²=c²d, e²h²=h², h³=c³, b²i=i, di=d², ce²fi=cfi, e³fi=efi, e²fgi=fgi, cg²i=c³i, fg²i=c³fi, g⁴i=bg³i, i²=d², b²j=j, c³j=c³, cdj=c²d, d²j=d², de³j=dej, dfj=df, ce²fj=cfj, e³fj=efj, f²j=d², dgj=bdg², ce²gj=cgj, e³gj=egj, cfgj=bc²fj, cg²j=c³, fg²j=c³f, g⁶j=bg⁵j, dhj=c²d, h²j=bcgj, ce²ij=cij, e³ij=eij, e²fij=fij, g²ij=c³i, e²hij=hij, cj²=c³, dj²=dg², ej²=bc²j, g²j²=g⁴j, hj²=c³, fij²=bc²efij, j³=g⁴j, b²k=k, c²k=bcegj, d²k=bd², cdek=c²d, de²k=bde³g, dfk=bdf, f²k=bcf², cgk=c³, g²k=bcg², h²k=bcegj, e²fik=fik, djk=bc²d, ce²jk=cjk, e³jk=ejk, cefjk=bcfjk, e²fjk=fjk, gjk=bcgj, ehjk=bhjk, e²ijk=ijk, j²k=bc³, ck²=cegj, dek²=bc²d, e³k²=ek², dgk²=degk, egk²=c³, fgk²=fgj², hk²=cegj, gik²=gij², jk²=cegj, k³=bc³, b²l=l, dl=df, c²fl=cfl, cefl=bcfl, e²fl=fl, f²l=acf², cgl=bc³l, fgl=bcfl, g³l=bg²l, ce²il=cil, e³il=eil, cfil=adf, g²il=c³il, e²hil=hil, h²il=be²gil, c²jl=beh²l, ce²jl=cjl, e³jl=ejl, fjl=cfl, gjl=bc³l, e²hjl=hjl, e²ijl=ijl, ij²l=be²gil, fkl=bcfl, e²gkl=c³l, hkl=bj²l, egikl=bc³il, jkl=bhjl, ek²l=eh²l, gk²l=egkl, ik²l=be²gil, l²=d², b²m=m, cm=bc², d²m=bd², dem=bde²g, e³m=em, dfm=bdf, f²m=bcf², dgm=dg², egm=bceg, g²m=g³j, hm=bc², e²fim=fim, fgim=bcfgi, djm=bdg², ejm=bcej, fgjm=c²fj, fijm=bcfij, j²m=g⁵j, dkm=c²d, e²km=km, gkm=bc³, jkm=bcjk, k²m=bc³, flm=bcfl, glm=c³l, e²ilm=ilm, ijlm=bcijl, klm=bce²kl, dm²=dg², fgm²=bc³f, gim²=gij², fjm²=c²fj, gjm²=g⁵j, ijm²=c²ij, km²=bc³, jlm²=beh²l, m³=g⁵j, b²n=n, c²n=cegj, cdn=c²d, d²n=d², ce²n=cn, de²n=de²j, dfn=df, f²n=bcef², cgn=bc³, dgn=bc²d, e³gn=egn, fgn=cfjk, g³n=bc³, hn=cn, e³in=ein, e²fin=fin, g²in=c³i, cjn=cegj, djn=c²d, e³jn=ejn, fjn=efgj, gjn=bc³, e²ijn=ijn, j²n=c³, ckn=hjk, dkn=dhk, e³kn=ekn, gkn=c³, jkn=bcegj, k²n=bhjk, cln=e³gl, e³ln=eln, fln=cfl, gln=bc³l, e²iln=iln, jln=e³gl, ekln=be²gl, ikln=begil, dmn=bc²d, e²mn=mn, gmn=c³, jmn=bcegj, kmn=bhjk, lmn=be³gl, m²n=c³, dn²=c²d, e³n²=en², fn²=bc²efj, egn²=c³, g²n²=c³, gin²=gij², jn²=c³, kn²=bcn², ln²=be²gl, mn²=bcn², n³=c³, b²o=o, c³o=c²o, do=d², c²eo=bc²o, fo=df, cego=c²o, ho=co, io=d², cjo=cg²o, e²jo=ce²o, gjo=g³o, j²o=g⁴o, ceko=c²o, e²ko=bce²o, egko=cko, jko=bcg²o, ek²o=bc²o, gk²o=cko, lo=df, emo=bceo, gmo=g⁴o, jmo=g⁵o, kmo=c²o, m²o=g⁶o, cno=e³go, e³no=eno, egno=c²o, ejno=e²go, ekno=be²go, mno=be³go, en²o=be³go, gn²o=cko, o²=d², b²p=p, c²p=c³, dp=dg², cep=bcp, e³p=ep, cfp=bcfjk, f²p=d², cgp=bc³, egp=c³, fgp=fgj², g²p=g⁴j, hp=cp, e²fip=fip, cjp=c³, ejp=cgj, gjp=gm², fijp=bc²efij, j²p=bg⁵j, kp=bcp, e²lp=belp, flp=cfl, glp=bc³l, eilp=bilp, jlp=begkl, emp=cp, gmp=bg⁵j, fimp=cfijk, jmp=g⁵j, ilmp=bcilp, m²p=bg⁵j, np=bcgj, op=g⁴o, cp²=c³, ep²=bc³, fp²=bfgj², gp²=g⁵j, ip²=bgij², jp²=bg⁵j, lp²=begkl, mp²=g⁵j, p³=bg⁵j, b²q=q, c²q=bc³, cdq=cdk, d²q=bd², ceq=bc²ej, deq=dk², dfq=bdf, f²q=bd², cgq=c³, e²gq=bcgj, efgq=bfjp, dg²q=bc²d, fg²q=bc³f, g³q=g²n, dhq=dhk, ehq=cegj, h²q=bc³, cfiq=bc²fij, e²fiq=fiq, fgiq=c²fij, g²iq=bc³i, hiq=bgijm, cjq=bc³, djq=bc²d, ejq=bc²ej, fjq=bc²fj, gjq=g²n, hjq=bc³, ijq=bc²ij, j²q=bc³, ckq=c³, dkq=dk², ekq=cgj, fkq=fj², hkq=c³, ikq=ijp, jkq=c³, k²q=bc³, e³lq=elq, flq=bcfl, glq=begkl, hlq=egkl, cilq=begil, e²ilq=ilq, jlq=eh²l, klq=begkl, dmq=c²d, emq=c²ej, fmq=c²fj, gmq=bc³, imq=c²ij, jmq=c³, kmq=bc³, lmq=beh²l, m²q=bc³, cnq=bc³, dnq=degk, enq=bcgj, fnq=bfjp, inq=bijp, jnq=g²nq, knq=c³, lnq=egkl, mnq=c³, n²q=bc³, coq=cko, eoq=c²o, joq=g²oq, koq=k²o, moq=g²no, gnoq=k²o, pq=bc³, cq²=c³, dq²=c²d, eq²=bc³, fq²=c³f, hq²=c³, giq²=gij², jq²=g²q², kq²=bc³, lq²=begkl, mq²=g²nq, nq²=c³, goq²=noq, q³=bc³, b²r=r, c³r=c²r, c²dr=d², d²r=ad², c²er=bc²r, cder=acef²i, fr=cf², gr=bc²r, hr=cr, ir=afil, jr=ce²r, ekr=c²r, k²r=c²r, lr=d², mr=bc²r, cnr=c²r, enr=cer, knr=ckr, n²r=c²r, or=df, pr=c²r, cqr=ckr, eqr=c²r, kqr=c²r, nqr=bc²r, q²r=c²r, r²=d², b²s=s, cs=hjk, d²s=bd², des=c²d, e³s=es, dfs=bdf, f²s=bd², dgs=bds, egs=bc³, fgs=c³f, g³s=bg²s, hs=hjk, e²fis=fis, gis=c³i, djs=ds, ejs=cegj, fjs=cfq, gjs=bg²s, ijs=bgijm, j²s=g²s, ks=cegj, ls=eh²l, dms=bds, ems=cgj, fms=bc²efj, gms=g²s, ims=cegij, jms=bg²s, m²s=g²s, ns=hjk, os=g⁵o, ps=g²s, qs=c³, rs=bc²r, ds²=c²d, es²=bc³, fs²=c³f, gs²=bs², is²=c³i, js²=s², ms²=bs², s³=bs², b²t=t, ct=bcgj, d²t=d², det=cdk, dft=df, f²t=d², dgt=bc²d, egt=c³, fgt=bc³f, g⁴t=c³, ht=bcgj, e²fit=fit, g²it=bgij², djt=c²d, ejt=c²ej, fjt=c²fj, gjt=g³t, ijt=bciq, j²t=c³, dkt=dhk, ekt=cegj, fkt=cfq, gkt=c³, ikt=bgijm, jkt=bc³, k²t=c³, e²lt=bce²kl, flt=cfl, glt=bc³l, ilt=bcikl, jlt=bclq, klt=bc³l, dmt=bc²d, emt=cegj, fmt=bc²fj, gmt=c³, imt=cgij, jmt=bc³, kmt=c³, lmt=bc³l, m²t=c³, dnt=c²d, ent=bc³, fnt=c³f, gnt=gn², int=iq², jnt=c³, knt=bc³, lnt=c³l, mnt=bc³, n²t=c³, eot=cko, jot=g²ot, kot=cko, mot=g³ot, not=k²o, pt=c³, qt=gq², ert=ckr, krt=ckr, nrt=c²r, st=bc³, dt²=c²d, et²=bc³, ft²=c³f, g²t²=g²q², it²=c³i, jt²=g²q², kt²=bc³, lt²=c³l, mt²=g²nq, nt²=c³, ot²=oq², rt²=c²r, t³=c³, b²u=u, c²u=c²o, du=d², ceu=e²go, fu=df, gu=bc²o, hu=cu, iu=d², ju=e³go, cku=cko, eku=c²o, k²u=c²o, lu=df, mu=bc²o, cnu=c²o, enu=e²go, knu=cko, n²u=c²o, ou=d², pu=c²o, cqu=cko, equ=c²o, kqu=c²o, nqu=bc²o, q²u=c²o, ru=df, su=bc²o, etu=cko, ktu=cko, ntu=c²o, t²u=c²o, u²=d², b²v=v, c²v=c³, dv=c²d, cev=bcegj, e²v=emn, fv=efmn, gv=bs², hv=cv, civ=gijm, cjv=c³, ejv=bcegj, ijv=bcgij, j²v=s², ckv=bc³, ekv=bhjk, jkv=bc³, k²v=c³, clv=begkl, elv=kln, jlv=c³l, klv=egkl, mv=bs², nv=bcen², cov=bcko, eov=kno, jov=bg⁷o, kov=cko, pv=s², qv=bc³, rv=c²r, sv=bs², tv=c³, uv=c²o, v²=s², b²w=w, cw=bcegj, d²w=bd², dew=c²d, e³w=ew, fw=befgj, dgw=c²d, egw=bc³, g⁴w=g²nq, hw=bcegj, giw=bgip, djw=bc²d, ejw=c³, g²jw=g²nq, ijw=biq², j²w=g²nq, kw=cegj, glw=begkl, ilw=bcilp, jlw=egkl, dmw=c²d, emw=cgj, gmw=g²nq, imw=begiq, jmw=c³, lmw=begkl, m²w=bc³, nw=gn², eow=be²go, jow=g²ow, mow=g³ow, pw=g²nq, qw=g²q², rw=ckr, sw=c³, tw=gt², uw=cko, vw=bc³, w²=t², b²x=x, cx=cr, d²x=ad², dex=der, fx=d², gx=bc²r, hx=ce²r, ix=df, jx=ce²r, ekx=c²r, k²x=c²r, lx=d², mx=bc²r, nx=ce²r, ox=df, px=c²r, qx=kx, rx=d², sx=bc²r, etx=ckr, ktx=bc²r, t²x=c²r, ux=df, vx=c²r, wx=ckr, x²=d², b²y=y, cy=bnt, dy=bc²d, e²y=bcegj, efy=c²fj, f²y=bd², egy=gn², fgy=c³f, g²y=bs², hy=bnt, jy=bs², eky=bc³, fky=c³f, gky=g²nq, iky=bgij², k²y=bc³, ely=c³l, fly=bcfl, gly=c³l, ily=bgikl, kly=begkl, my=s², eny=c³, fny=bc³f, iny=biq², kny=c³, lny=bc³l, n²y=bc³, eoy=k²o, koy=k²o, noy=cko, py=bs², qy=gny, ry=bc²r, sy=s², ty=bc³, uy=bc²o, vy=bs², wy=c³, xy=bc²r, y²=s², b²z=z, cz=c³, dz=c²d, ez=bcejk, fz=bcfjk, g⁴z=g²q², hz=c³, g²iz=bgij², g²jz=g²q², ijz=iq², j²z=g²q², kz=bc³, glz=bc³l, ilz=egil, jlz=begkl, gmz=gnq, imz=biq², jmz=g²nq, lmz=egkl, m²z=c³, nz=c³, joz=g²oz, moz=g³oz, pz=gnq, qz=g²nq, rz=c²r, sz=g²nq, tz=g²q², uz=c²o, vz=c³, wz=gt², xz=c²r, yz=bc³, z²=t², b²A=A, c³A=c²A, dA=d², c²eA=bc²A, fA=drt, gA=bc²A, hA=ce²A, iA=d², jA=ce²A, ekA=c²A, k²A=c²A, lA=df, mA=bc²A, nA=ce²A, oA=d², pA=c²A, cqA=ckA, eqA=c²A, kqA=c²A, q²A=c²A, rA=df, sA=bc²A, etA=ckA, ktA=bc²A, t²A=c²A, uA=d², vA=c²A, wA=ckA, xA=df, yA=bc²A, zA=c²A, A²=d², b²B=B, c²B=c³, dB=c²d, ceB=bc³, e²B=bhjk, fB=bcfjk, cgB=bg²q², egB=g²q², g³B=bs², hB=cB, ciB=bgij², eiB=ikv, giB=gij², jB=g²B, kB=gt², clB=begkl, elB=egkl, glB=bc³l, ilB=gikl, mB=bs², nB=gnq, coB=bnoq, eoB=noq, goB=oy, pB=s², qB=g²nq, rB=c²r, sB=bs², tB=c³, uB=c²o, vB=s², wB=bc³, xB=c²r, yB=bs², zB=c³, AB=c²A, B²=s², b²C=C, cC=bc³, dC=bc²d, eC=c³, fC=bc³f, g⁴C=gt², hC=bc³, iC=giz, gjC=g³C, j²C=gt², kC=c³, lC=egkl, gmC=gt², jmC=g²q², m²C=g²nq, nC=bc³, joC=g²oC, moC=g³oC, pC=gt², qC=c³, rC=bc²r, sC=g²q², tC=g²nq, uC=bc²o, vC=g²nq, wC=g²q², xC=bc²r, yC=c³, zC=gt², AC=bc²A, BC=bc³, C²=t²>

P = {a, b², c, c², c³, bd, acd, ac²d, d², be, bce, bc²e, ade, e², ce², bde², acde², be³, ade³, f, acf, ac²f, ac³f, bdf, aef, bcef, abc²ef, e²f, ace²f, ae³f, f², cf², bef², bcef², bg, bcg, dg, eg, ceg, adeg, be²g, bce²g, e³g, ade³g, bfg, abcfg, aefg, acefg, be²fg, ae³fg, g², cg², bdg², fg², bg³, g⁴, bg⁵, g⁶, bg⁷, h, adh, beh, e²h, h², beh², bi, aci, ac²i, ac³i, aei, abc²ei, be²i, ace²i, ae³i, fi, c²fi, c³fi, aefi, cefi, e²fi, bf²i, acf²i, aef²i, abcgi, acegi, abce²gi, bcfgi, befgi, bg²i, ahi, ae²hi, ah²i, abeh²i, j, cj, c²j, bdj, bej, bcej, bc²ej, abdej, e²j, ce²j, ade²j, be³j, afj, acfj, ac²fj, abefj, abcefj, abc²efj, ae²fj, bgj, bcgj, egj, cegj, be²gj, bfgj, aefgj, abe²fgj, g²j, bg³j, g⁴j, bg⁵j, hj, behj, e²hj, aij, acij, ac²ij, abceij, abc²eij, ae²ij, bfij, bcfij, efij, bc²efij, abcgij, aegij, acegij, abe²gij, fgij, ahij, abehij, j², fj², bgj², bfgj², bij², bk, bck, adk, ek, cek, bdek, be²k, bce²k, e³k, bfk, bcfk, efk, acefk, abe²fk, abce²fk, e³fk, gk, adgk, begk, e²gk, be³gk, afgk, befgk, ae²fgk, abe³fgk, bhk, ehk, be²hk, beik, aceik, abe²ik, abce²ik, befik, bcefik, agik, ae²gik, abe³gik, aehik, abe²hik, bjk, bcjk, ejk, cejk, be²jk, abfjk, abcfjk, aefjk, bhjk, abijk, abcijk, aeijk, aceijk, befijk, abhijk, k², bdk², bek², e²k², fk², abefk², ae²fk², bgk², bik², abeik², ae²ik², fik², l, acl, ac²l, ac³l, ael, bcel, abc²el, e²l, ace²l, ae³l, fl, cfl, befl, bgl, aegl, be²gl, ae³gl, g²l, ahl, behl, ae²hl, ah²l, abeh²l, il, c²il, c³il, ceil, e²il, abfil, aefil, bgil, be²gil, ehil, ajl, acjl, bejl, abcejl, ae²jl, ahjl, abehjl, bijl, bcijl, eijl, j²l, bkl, bckl, ekl, acekl, abe²kl, abce²kl, e³kl, agkl, begkl, beikl, k²l, bm, dm, em, be²m, abfm, efm, abe²fm, gm, fgm, abim, abe²im, efim, bjm, bfjm, gjm, ijm, km, bekm, afkm, abefkm, aikm, abeikm, ablm, elm, abe²lm, eilm, bjlm, m², bem², e²m², fm², abefm², ae²fm², bgm², bim², abeim², ae²im², fim², befim², jm², lm², abelm², ae²lm², ilm², beilm², n, cn, adn, ben, bcen, e²n, be³n, afn, acfn, befn, abcefn, ae²fn, abe³fn, bgn, egn, be²gn, g²n, bin, acin, aein, bfin, aefin, cefin, abe²gin, jn, bejn, e²jn, aijn, bkn, ekn, be²kn, bfkn, aefkn, abe²fkn, abe²ikn, fikn, befikn, ln, beln, e²ln, bkln, bmn, emn, abfmn, aefmn, abimn, efimn, n², cn², ben², bcen², e²n², bgn², bin², acin², aein², bo, aco, ac²o, aeo, be²o, ace²o, ae³o, go, abcgo, aego, ae³go, bg²o, acg²o, g³o, bg⁴o, g⁵o, bg⁶o, g⁷o, bjo, ako, beko, agko, bk²o, mo, bno, ag²no, ajno, bn²o, p, cp, bep, e²p, afp, abefp, ae²fp, bgp, aip, acip, abeip, ae²ip, bfip, efip, jp, fjp, bijp, alp, aclp, abelp, bilp, bmp, bfmp, blmp, p², bq, bcq, adq, eq, be²q, e³q, bfq, bcfq, aefq, abe²fq, ae³fq, gq, adgq, begq, afgq, bg²q, bhq, iq, aeiq, abe²iq, ae³iq, bjq, kq, bgkq, blq, bclq, aelq, abe²lq, mq, bnq, gnq, bg²nq, oq, bgoq, noq, q², bgq², g²q², biq², boq², ar, acr, ac²r, dr, cdr, ber, bcer, ae²r, ace²r, de²r, be³r, bkr, bckr, anr, dnr, bqr, bs, es, be²s, bfs, aefs, abe²fs, gs, bg²s, aeis, abe²is, befis, bjs, ms, s², t, adt, bet, e²t, be³t, aft, beft, ae²ft, abe³ft, bgt, g²t, bg³t, bit, ae²it, abe³it, bfit, git, jt, bkt, lt, belt, bmt, nt, bot, got, bg²ot, art, drt, t², bgt², au, acu, ae²u, anu, atu, v, cv, bev, abiv, jv, bkv, lv, bov, bw, abdw, ew, be²w, gw, bg²w, g³w, iw, abe²iw, bjw, gjw, blw, elw, abe²lw, mw, ow, bgow, g²ow, bg³ow, ax, dx, bex, ae²x, be³x, bkx, atx, dtx, by, ey, abfy, gy, iy, beiy, ky, bly, bny, gny, oy, bgoy, z, bgz, g²z, bg³z, biz, giz, jz, bgjz, lz, bmz, boz, goz, bg²oz, g³oz, aA, acA, ac²A, ae²A, ace²A, atA, B, cB, beB, bgB, g²B, biB, lB, boB, bC, gC, bg²C, g³C, bjC, mC, oC, bgoC, g²oC, bg³oC}

Phi = 1 a b c d b² 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 x

Monoid Structure