Details Page for 0.316

Complete Solution is Known:

Period:  
Preperiod:  
Quotient Size:   8704
P-Portion Size:   1668
Tame?   No

MSV File: q-0.316.msv

Growth Pattern:

Heap   Q-Size   P-Size
121
262
4123
74812
914831
1119242
1245296
13736152
14804165
152084409
162532498
173228638
183760740
194348831
204816936
2163761211
2284441609
2387041668

(Click on a heap to see details)

Details for Q21(0.316):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t | a2=1, b5=b3, b3c=b3, c2=c, b3d=b4, d2=1, b2e=b3, ce2=bce, e4=de3, b2f=ab3, bef=ab3, cf2=abcf, e2f2=b4, bf3=ab4, ef3=abdf2, f4=def2, b3g=b3, b2cg=b2c, bceg=bce, be2g=ade3f, bcfg=bcf, cefg=cef, e2fg=e2f, f2g=f2, b2g2=b2c, cg2=cg, bfg2=bfg, beg3=beg2, e2g3=e2g2, fg3=fg2, g4=g3, b4h=b2h, b2ch=b2h, b2dh=b3h, ceh=bch, be2h=b3h, bcfh=bfh, e2fh=ab3h, bf2h=b3h, b2gh=b2h, cgh=ch, begh=b2h, e3gh=de2gh, bfgh=bfh, efgh=efh, bg2h=bgh, eg2h=egh, fg2h=fgh, ch2=b2h2, beh2=b2h2, e2h2=b2h2, bfh2=ab2h2, f2h2=b2h2, bgh2=adefh2, egh2=eh2, g2h2=gh2, bh3=ab3h2, eh3=defh2, fh3=b3h2, h4=b2h2, b2i=b2g, bci=bcg, bei=beg, cei=ceg, e2i=e2g, bfi=bfg, cfi=cfg, efi=efg2, f2i=f2, gi=g2, bhi=bgh, chi=ch, ehi=egh, fhi=fgh, h2i=gh2, i2=g2, bj=abe, cj=ace, ej=ae2, fg2j=fgj, g3j=g2j, f3hj=b2h, g2hj=ghj, fgh2j=fh2j, h3j=dfh2j, fij=fgj, hij=ghj, f2j2=adf2j, fgj2=fj2, h2j2=b2h2, ij2=gj2, fj3=adfj2, ghj3=adghj2, j4=adj3, b3k=b3, cek=bck, cfk=abck, e2fk=ab3, bf2k=b3, ef2k=bf2, e3g2k=ade3f, efg2k=efgk, b2hk=b2h, bchk=abdfh, behk=b2h, bfhk=ab2h, efhk=adef2h, f3hk=aef2h, bghk=abdfh, e2ghk=b2h, fghk=fhk, eh2k=adefh2, fh2k=ab3h2, h3k=ab2h2, bik=bgk, cik=cgk, fik=fgk, hik=ghk, f2jk=adf3j, fgjk=fjk, fhjk=adf2hj, h2jk=adfh2j, b2k2=b4, ck2=b2ck, be3k2=bde2k2, bfk2=ab4, efk2=ab4, f2k2=b4, begk2=b4, e2gk2=bde2k2, fg2k2=abf2, bhk2=b3h, e3hk2=de2hk2, fhk2=ab3h, eghk2=b3h, g3hk2=def2h, h2k2=bdh2k, fjk2=b4, hjk2=aehk2, j2k2=e2k2, bk3=bdek2, ek3=e3k2, fk3=ab3, g3k3=bdf2, hk3=dehk2, jk3=ae3k2, k4=de3k2, b2l=ab4, bcel=ab2ck, be2l=de3f, e3l=ae3g2, cfl=abcl, bf2l=ab3, ef2l=abf2, f3l=ef2, cegl=abcgk, e2gl=e2l, bfgl=bdf2, beg2l=begl, g3l=g2l, chl=achk, behl=ab2h, e2hl=ae2gh, bfhl=b2h, efhl=def2h, f2hl=df3h, fghl=fhl, bh2l=abh2k, eh2l=defh2, fh2l=b3h2, gh2l=dfgh2, h3l=b2h2, bil=bg2l, cil=cgl, eil=eg2l, fil=fg2l, hil=g2hl, fgjl=fjl, g2jl=gjl, h2jl=dfh2j, ijl=gjl, gj2l=j2l, fhj2l=adfhjl, hj3l=adhj2l, e2kl=ade2fl, bfkl=b4, efkl=bdf2, f2kl=df3k, cgkl=ab2ck, begkl=abdg3k2, bg2kl=bgkl, eg2kl=egkl, fg2kl=fgkl, bhkl=ab3h, fhkl=df2hk, eghkl=aef2h, g2hkl=ghkl, h2kl=abdh2k, ikl=gkl, fjkl=adf2jl, hj2kl=adghjkl, j3kl=adj2kl, ek2l=bdekl, fk2l=b3, bgk2l=ab3, ghk2l=ab2h, jk2l=abdekl, k3l=bdk2l, cl2=b4, e2l2=de3g2, begl2=ae3f, eg2l2=e3g2, bghl2=bhl2, eghl2=de2gh, h2l2=b2h2, il2=g2l2, fjl2=dfj2l, gjl2=aj3l, hjl2=dhj2l, j2l2=dj3l, bekl2=abdk2l, egkl2=ade3f, g2kl2=gkl2, ehkl2=adhk2l, k2l2=bdkl2, bl3=abgl2, el3=aegl2, f2l3=adf2jl, fgl3=fj2l, g2l3=gl3, fhl3=adfhjl, jl3=j3l, fkl3=f2jl, gkl3=kl3, l4=agl3, b2m=b3, cem=bce, e2m=ade3f, bfm=ab3, efm=aeg2k2, f3m=abdg3k2, cgm=bcg, begm=b3, bg2m=bgm, eg2m=egm, fg2m=fgm, g3m=g2m, bhm=b2h, chm=bch, ehm=b2h, f2hm=b3h, fghm=fhm, g2hm=ghm, h2m=dfh2j, im=gm, fjm=af2j, g2jm=gjm, gj2m=j2m, hj2m=adghjm, j3m=adj2m, ckm=bcgk, bekm=b3, f2km=bg3k2, egkm=beg2k, fgkm=fkm, fhkm=ab2h, ghkm=adfhm, hjkm=df2hj, k2m=bgk2, blm=abdg3k2, clm=bcgl, f2lm=aeg3k2, glm=lm, fhlm=b2h, hjlm=dghjkl, eklm=abdg3k2, fklm=deg3k2, hklm=ab3h, j2klm=adjklm, el2m=ae3f, jl2m=dj2lm, fl3m=df2jl, hl3m=ahl2m, bm2=b3, cm2=b2c, em2=b3, fm2=adf3j, g2m2=gm2, hm2=adf2hj, gjm2=jm2, j2m2=adjm2, gkm2=km2, jkm2=adf3j, lm2=ajklm, m3=df3j, b3n=b2h, be2n=e2gh, cfn=abcn, e2fn=ae2gh, bf2n=b2h, ef2n=b2h, f3n=ab2h, b2gn=abfn, cegn=cen, bfgn=ab2cn, beg2n=aefgn, e2g2n=e2gn, efg2n=efgn, b2hn=b3h2, chn=b3h2, e3hn=de2hn, bfhn=ab3h2, efhn=ab3h2, f2hn=b3h2, e2ghn=e2hn, bh2n=ab2h2, eh2n=efh2, fh2n=b2h2, h3n=b3h2, in=gn, gh2jn=fh2j, g2j2n=gj2n, fhj2n=adfghjn, ghj2n=hj2n, hj3n=adhj2n, bckn=chk, efkn=bfkn, f2kn=abdfh, cgkn=ckn, begkn=abfkn, e3gkn=e2gh, bhkn=bdh2k, e2hkn=b3h2, fhkn=ab2h2, eghkn=b2h2, h2kn=ab3h2, ghjkn=efh2, fj2kn=f2jn, hj2kn=b3h2, bek2n=b3h, e2k2n=de2hk2, egk2n=bgk2n, fgk2n=hk2l, bg2k2n=ahk2l, ehk2n=b2h2, g2hk2n=bh2k, gk3n=bdgk2n, celn=achk, bfln=b3h, efln=e2gkn, f2ln=df2jn, cgln=cln, begln=ae2gkn, fgln=fln, g2ln=gln, bhln=abghn, fhln=dfghjn, eghln=ade2hn, h2ln=b3h2, ghjln=dhj2n, fj2ln=afj2n, hj2ln=ahj2n, j3ln=agj3n, ckln=bdfh, bekln=dhk2l, fkln=af2jn, egkln=ae2gh, ehkln=abdh2k, gjkln=agj3kn, hjkln=bdh2k, j2kln=dgj3kn, bk2ln=ab2h, gk2ln=bdgkln, hk2ln=ab3h2, el2n=e3gn, fl2n=fj2n, gl2n=l2n, hl2n=aghln, jl2n=gj3n, bkl2n=abgkln, l3n=al2n, bemn=beh, f2mn=b2h, bgmn=b2cn, egmn=aefgn, fgmn=af2n, fhmn=ab3h2, ghmn=bghn, bkmn=abfkn, fkmn=bdfh, hkmn=bdh2k, j2kmn=dghjkl, elmn=ae2gkn, flmn=adf2jn, hlmn=abghn, j2lmn=aj2mn, jklmn=ghjkl, kl2mn=aklmn, jm2n=adghjkl, km2n=abdfh, cn2=b2h2, e3n2=de2n2, efn2=ehln, begn2=aehln, e2gn2=e2n2, eg2n2=de2n2, fg2n2=fgn2, g3n2=g2n2, e2hn2=ade2hn, fhn2=df2n2, eghn2=ae2hn, g2hn2=ghn2, h2n2=abehn2, fjn2=adfgn2, j2n2=adg2jn2, b2kn2=dghk2n, e2kn2=de2hn, bfkn2=abdh2k, fgkn2=adf2n2, bg2kn2=abghn2, ehkn2=bdehn2, ghkn2=bdghn2, g2jkn2=aghjn2, hjkn2=abdehn2, bk2n2=ghk2n, ek2n2=bdekn2, fk2n2=abh2k, gk2n2=bdgkn2, hk2n2=abdh2k, jk2n2=abdekn2, k3n2=dghk2n, eln2=ade2n2, fln2=afgn2, gln2=ag2n2, hln2=aghn2, jln2=ag2jn2, bkln2=bghn2, k2ln2=bdghn2, l2n2=g2n2, g2mn2=gmn2, gjmn2=adghjn2, hjmn2=bdh2k, ekmn2=abehn2, gkmn2=abghn2, jkmn2=behn2, lmn2=agmn2, m2n2=bdh2k, b2n3=ab3h2, e2n3=ade2n2, bfn3=b3h2, f2n3=ab3h2, bgn3=afn3, egn3=ae2n2, fgn3=de2hn, g2n3=ade2n2, ehn3=adehn2, ghn3=e2hn, jn3=aen3, bkn3=abhn3, fkn3=b2h2, gkn3=adfn3, hkn3=bdhn3, k2n3=abdhn3, ln3=agn3, emn3=ehn2, fmn3=b3h2, gmn3=ade2hn, hmn3=abehn2, kmn3=bdmn3, n4=adn3, b3o=b4, b2co=b2o, be2o=ae3f, e3o=de3g, e2fo=e3f, bf2o=bdf2, b2go=b2o, cgo=co, bego=beo, bfgo=bfo, efgo=efo, g2o=go, b2ho=b3h, cho=cdh, beho=b3h, e2ho=de2gh, bfho=bdfh, f2ho=df2h, gho=ho, bh2o=b2h2, eh2o=b2h2, io=go, f2jo=df2j, fgjo=fjo, fhjo=dfghj, h2jo=dgh2j, fj2o=dfj2, hj2o=dghj2, j3o=dgj3, beko=b2ko, bhko=abfh, fhko=dfhk, h2ko=ah3o, bk2o=b4, ek2o=bde2k2, fk2o=ag2k3, hk2o=ef2h, jk2o=abde2k2, gk3o=bf2, belo=ae2gko, celo=abcko, bflo=bf2, bglo=blo, eglo=elo, fglo=flo, bhlo=bfh, h2lo=dfh2o, gjlo=jlo, bklo=abdg3k2, cklo=ab2ko, ehklo=adef2h, jklo=aj2kl, k2lo=adg2k3, bl2o=ae3f, el2o=de3g2, gl2o=l2o, jl2o=adj3l, l3o=aj3l, bmo=b2o, cmo=bco, emo=beo, f2mo=f3j, gmo=mo, fhmo=dfhm, hjmo=dghjm, j2mo=dj2m, hkmo=afhm, flmo=f2jl, hlmo=dgjkmn, klmo=ajklm, l2mo=adj2lm, jm2o=djm2, km2o=afkmo, b2no=b2cdn, cno=cdgn, e2no=de2gn, bfno=ab2cdn, efno=abeno, f2no=df2n, egno=eno, bhno=b3h2, ehno=e2hn, fhno=afghjn, h2no=fh2o, fjno=dfgjn, gjno=jno, j2no=dgj2n, fkno=dfgkn, bgkno=cdhk, hkno=aefh2, gk2no=abfh, k3no=b2h, elno=degln, flno=dfln, hlno=adhj2n, jlno=dgjln, gklno=adgj2kn, l2no=agj3n, fmno=adf2n, hmno=b3h2, jkmno=dgjkmn, m2no=dgm2n, n2o=agjn2, b2o2=b2do, beo2=bdeo, ceo2=cdeo, e2o2=de2go, bcfo2=bcdfo, go2=o2, bho2=bdho, eho2=deho, fho2=dfho, h2o2=dh2o, jo2=dgjo, cko2=cdko, bfko2=bdfko, k3o2=bdf2, hklo2=dhklo, l2o2=dl2o, fmo2=dfmo, hmo2=dhmo, kmo2=dkmo, m2o2=dm2o, eno2=deno, fno2=dfgno, bkno2=chk, k2no2=abdfh, lno2=dglno, mno2=dmno, o3=do2, b2p=ab4, cep=bcp, cfp=abcp, e2fp=b3, bf2p=ab3, ef2p=abdfp, begp=adeg3k2, e2gp=ade2fl, bfgp=bfp, efgp=efp, bg2p=bgp, eg2p=egp, fg2p=fgp, g3p=g2p, bhp=ab3h, chp=ab2h, efhp=b2h, f2hp=adef2h, fghp=fhp, g2hp=ghp, h2p=efh2, ip=gp, fjp=df2j, g2jp=gjp, ghj2p=adghjp, gj3p=adgj2p, ckp=ab2ck, bekp=bdk2l, e2kp=bde2p, bfkp=b4, efkp=bfp, f3kp=bdfp, fgkp=fkp, ehkp=dhk2l, fhkp=ef2h, gjkp=afj2k, hjkp=af2hj, bk2p=bk2l, ek2p=bk2l, fk2p=b3, g2k2p=bdgkp, hk2p=hk2l, jk2p=abk2l, k3p=bdk2l, clp=ackl, e2lp=ae3f, bflp=ab4, eflp=abdf2, f2lp=efp, bglp=adg2k2l, g2lp=glp, fhlp=eghp, eghlp=adg2jk2n, hjlp=dfhjl, j2lp=dfj2l, bklp=abk2l, egklp=bf2, hklp=adeghp, jklp=af2jl, k2lp=abdk2l, bl2p=abkl2, egl2p=de3f, fgl2p=fl2p, ehl2p=dhk2l, ekl2p=bk2l, fkl2p=bf2, fl3p=af2jl, gl3p=l3p, kl3p=df2jl, bmp=ab4, cmp=bcgp, emp=adeg3k2, fmp=df2m, gmp=mp, hmp=f2hj, jmp=adf2j, klmp=eg3k2, l3mp=f2jl, m2p=af3j, cnp=abcen, e2np=ade2gh, fnp=af2jn, bgnp=bgkln, ehnp=abdh2k, ghjnp=dfghjn, j2np=dfj2n, egknp=ab2h, g2knp=afjkn, hknp=abh2k, k2np=abdgk2n, blnp=abgkln, elnp=e2gh, glnp=lnp, hlnp=aghnp, jlnp=fj2n, klnp=adf2jn, mnp=f2jn, en2p=ademn2, g2n2p=gn2p, ghn2p=f2n2, gjn2p=afgn2, hjn2p=adf2n2, bkn2p=abh2k, gkn2p=af2n2, jkn2p=dhn2p, ln2p=agn2p, n3p=admn3, bcop=ab4, beop=ab3, e2op=de3f, efop=abdop, gop=op, ehop=adef2h, jop=agj2p, bkop=abdfop, k2op=abfop, blop=bdf2, eklop=bdf2, hl2op=dfhjl, mop=df2j, bnop=ab3h, enop=ade2gh, hnop=adfghjn, knop=adfjkn, lnop=adfjln, co2p=abcdeo, bfo2p=bdf2, f3o2p=abo2p, ho2p=dhop, f2ko2p=deko2p, elo2p=delop, fklo2p=eko2p, cp2=b4, bep2=abdk2l, e2p2=abdk2l, bfp2=ab4, efp2=ab4, f2p2=bdf2, bgp2=bg3k2, fgp2=fp2, g2p2=gp2, ehp2=adhk2l, fhp2=aef2h, ghp2=adf3h, hjp2=dhk2l, j2p2=adgjp2, bkp2=abk2l, ekp2=abk2l, fkp2=abf2, hkp2=def2h, jkp2=adf3j, k2p2=abdk2l, blp2=bk2l, elp2=abg3k2, flp2=egp2, hlp2=adef2h, jlp2=f2jl, klp2=adegp2, l2p2=adl2mp, kmp2=bg3k2, lmp2=abg3k2, bnp2=ahk2l, enp2=ahk2l, gnp2=adf2jn, hnp2=bh2k, jnp2=f2jn, knp2=adhk2l, lnp2=df2jn, n2p2=f2n2, bop2=b4, eop2=bdf2, hop2=af3h, lop2=af2l2o, nop2=af2jn, fo2p2=dfop2, ko2p2=dkop2, bp3=bk2l, ep3=bk2l, fp3=bf2, gp3=bdo2p, hp3=hk2l, jp3=abk2l, kp3=abdf2, lp3=bdf2, mp3=ab3, np3=ab3h, op3=bo2p, p4=b4, b2q=b3, cq=bck, bfq=ab3, efq=ae2fl, f2q=af3k, begq=ade3f, e2gq=e3g2, bg2q=abegl, eg2q=ae2l, g3q=g2q, bhq=beh, eghq=e2gh, fghq=af2hk, g2hq=ghq, eh2q=b2h2, fh2q=abdh2k, gh2q=adefh2, h3q=abh2k, biq=bgq, eiq=ae2l, fiq=fg2q, hiq=ghq, jq=aeq, be2kq=abde2p, fkq=ag2k3, bgkq=bdg2k2, e2hkq=ade2hp, ghkq=ef2h, h2kq=b3h2, bek2q=abk2l, e2k2q=bdek2, egk2q=abdk2l, g2k2q=bg3k2, ehk2q=ahk2l, ik2q=bg2k2, gk3q=abk2l, elq=ade3g2, bglq=e3f, fhlq=def2h, h2lq=abh2k, ilq=g2lq, bklq=bdk2l, g2klq=gklq, hklq=dhk2l, k2lq=bk2l, l2q=egl2, bmq=b3, emq=ade3f, fmq=abg3k2, gmq=aelm, hmq=b2h, kmq=bdg2k2, lmq=e3f, m2q=b3, enq=ae2ln, bgnq=afnq, fgnq=ae2gkn, g2nq=aegln, fhnq=ab3h2, ghnq=de2hn, h2nq=ab2h2, hknq=abehn2, k2nq=bdknq, lnq=ae3gn, mnq=afnq, fn2q=ade2hn, gn2q=de2n2, hn2q=ehn2, bkn2q=abehn2, n3q=adn2q, boq=e2gko, eoq=ae2lo, fgoq=foq, fhoq=adf2hk, h2oq=b2h2, gkoq=aeklo, hkoq=def2h, k2oq=abdk2l, gloq=loq, hloq=dghlq, kloq=e3f, moq=e2gko, noq=adegln, ho2q=dhoq, ko2q=aeklo2, be2pq=bdk2l, e3pq=e3f, bgpq=abdg3k2, egpq=e3f, fgpq=fpq, g2pq=gpq, e2hpq=dhk2l, fhpq=b2h, ghpq=aef2h, bkpq=bdk2l, ekpq=bdepq, gkpq=aegp2, hkpq=dhk2l, k2pq=bk2l, blpq=abdk2l, flpq=bdgkp, hlpq=adhk2l, klpq=bg3k2, mpq=abdg3k2, bnpq=dhk2l, gnpq=ae2gh, hnpq=abdh2k, knpq=hk2l, n2pq=ae2hn, fopq=af2kop, hopq=adef2h, kopq=abdf2, bp2q=abdk2l, ep2q=abdk2l, fp2q=ab4, gp2q=bf2, hp2q=adhk2l, kp2q=abk2l, lp2q=ab3, np2q=b2h, op2q=bdf2, p3q=ab3, e3q2=e3g2, fq2=defgl2, bgq2=ade3f, egq2=e3g2, g2q2=de3g2, ghq2=e2gh, h2q2=b2h2, iq2=de3g2, ekq2=adepq, gkq2=bde2q2, bk2q2=abk2l, hk2q2=ahk2l, k3q2=abdk2l, lq2=ade3g2, mq2=ade3f, nq2=de3gn, oq2=e3g2, epq2=e2pq, gpq2=e3f, kpq2=bdpq2, p2q2=b4, eq3=e2q2, gq3=e3g2, kq3=adpq2, pq3=de3f, q4=de3g2, b2r=ab3, ber=abem, e2r=de3f, bfr=bf2, cfr=abcr, efr=def2o, f3r=ef2o, bcgr=bcr, cegr=cer, fg2r=fgr, g3r=g2r, bhr=bfh, chr=acdhk, ehr=defho, fhr=f2h, g2hr=ghr, h2r=dfh2o, ir=gr, fjr=f2j, g2jr=gjr, hjr=fghj, j2r=fj2, ckr=bckl, f2kr=f3k, ghkr=hkr, gjkr=adfj2k, bk2r=ab4, ek2r=ab4, fk2r=b4, gk2r=adg2k3, hk2r=ab3h, jk2r=b4, k3r=ab3, blr=abg2kr, clr=b3, f2lr=def2o, glr=lr, jlr=adfj2l, eklr=abg2kr, k2lr=b3, el2r=e3f, fl2r=df2l2o, hl2r=dfhl2o, l3r=fj2l, bmr=ab3, cmr=bcr, emr=ab3, fmr=df3j, g2mr=gmr, hmr=fhm, jmr=af2j, gkmr=af3j, lmr=df2jl, m2r=adf3j, cnr=bcln, f2nr=ab2h, fgnr=adf2jn, bg2nr=ab3h, ghnr=adfghjn, bknr=abdgk2n, eknr=abknq, fknr=adhk2l, g2knr=f2jn, hknr=ab2h2, jknr=djknp, k2nr=abgk2n, lnr=afj2n, mnr=afnr, bn2r=abmn2, en2r=aemn2, fn2r=f2n2, gn2r=fgn2, hn2r=dhn2p, jn2r=djn2p, n3r=amn3, bcor=bcdr, gor=or, bkor=abg3k2, jkor=afj2k, k2or=abdf2, mor=dgmr, bnor=ab2h, enor=ade2gkn, fnor=af2jn, hnor=afghjn, jnor=dgjnr, knor=df2jn, f2o2r=f3o2, ho2r=dhor, elo2r=adeklo2, no2r=dnor, bpr=bdfop, cpr=abckl, epr=abop, fgpr=fpr, g2pr=gpr, hpr=dfhop, jpr=df2j, fkpr=f2kp, gkpr=kpr, k2pr=b3, klpr=fklp, l2pr=dfl2op, mpr=f3j, npr=af2jn, flopr=df2opr, fo2pr=f2o2p, lo2pr=flo2p, p2r=dfop2, bqr=ab3, eqr=de3f, fqr=af3k, g2qr=gqr, hqr=af2hk, kqr=bgkr, mqr=ab3, nqr=ade2hq2, lo2qr=adeklo2, pqr=af2kp, q2r=de3f, br2=bg3k2, cr2=b4, f2r2=ef2o, egr2=er2, fgr2=fr2, g2r2=gr2, ghr2=hr2, jr2=f2j, ekr2=bg3k2, k2r2=b4, elr2=abg3k2, fklr2=bg3k2, hklr2=g2jk2n, kl2r2=bdg3k2, mr2=df3j, nr2=fnr, eor2=aeko2r, flor2=afklo2r, hlor2=adhklor, l2or2=adkl2or, fko2r2=deko2r, fpr2=f2pr, gpr2=pr2, lpr2=flpr, qr2=afkr2, er3=ab4, gr3=r3, hr3=ahkor2, kr3=abg3k2, flr3=ab4, l2r3=ab3, or3=ako2r2, pr3=akopr2, r4=b4, b2s=b4, bcs=abckl, bes=bel2, ces=abckl, e2s=de3g2, bfs=ab4, cfs=bckl, efs=efgl2, f3s=abdfp, cgs=b2c, egs=e3g2, g2s=gs, chs=b2h, ehs=ehl2, f2hs=b2h, bghs=b3h, bh2s=b3h2, fh2s=ab3h2, h3s=ab2h2, bis=bgs, eis=e3g2, fis=fgs, his=ghs, f2js=adjklm, fhjs=dhjkl, h2js=hjmn, ijs=gjs, j2s=adgjs, cks=b2ck, fks=adjklm, bhks=b3h, ghks=aklmn, h2ks=b2h2, iks=gks, hjks=aghjkl, bk2s=abk2l, ek2s=abk2l, gk2s=bdgks, hk2s=ahk2l, jk2s=bk2l, k3s=abdk2l, bls=abgs, cls=ab4, els=ae3g2, fls=dfgjs, gls=ls, h2ls=ab2h2, ils=ls, jls=agjs, hkls=klmn, k2ls=abdgks, l2s=als, bms=b4, cms=b3, ems=ae3f, f2ms=b3, gms=dfgjs, fhms=ab2h, jms=afgjs, kms=djklm, lms=adfgjs, m2s=jklm, cns=bcmn, ens=e3gn, f2ns=ghjkl, bhns=adhjmn, fghns=efh2, h2ns=dfhns, fgjns=aghjs, ghjns=ade2hn, gjkns=jkns, k2ns=bdkns, fmns=ahjkl, gn2s=e2n2, jn2s=ade2n2, bkn2s=bh2k, hkn2s=abdh2k, ln2s=ae2n2, hmn2s=abh2k, n3s=ade2n2, bos=ae3f, cos=b2o, eos=de3g2, gos=os, hos=aghjs, jos=dgjs, k2os=b3, los=gjs, mos=fgjs, fnos=ghjs, ko2s=dkos, no2s=dnos, bps=abks, cps=ab4, eps=aeks, fps=djklm, ghps=klmn, gjps=dfgjs, hjps=ghjkl, gkps=ajklm, hkps=hk2l, jkps=djklm, k2ps=bdk2l, lps=agps, mps=adjklm, jnps=adghjs, knps=ahjkl, n2ps=adegkn2, ops=adfgjs, gp2s=jklm, hp2s=ahk2l, jp2s=adjklm, kp2s=abdk2l, np2s=ghjkl, p3s=ab4, bqs=bel2, eqs=de3g2, fqs=e3f, gqs=e3g2, hqs=ehl2, iqs=e3g2, kqs=eks, lqs=ae3g2, mqs=ae3f, nqs=e3gn, oqs=de3g2, pqs=e2pq, q2s=de3g2, brs=ab4, crs=ab3, ers=e3f, frs=f2s, hrs=ahjkl, jrs=fgjs, krs=adjklm, lrs=dfgjs, mrs=ajklm, nrs=adfjns, prs=djklm, qrs=e3f, gr2s=r2s, r3s=ab3, cs2=b4, es2=e3g2, fs2=adfjs, bhs2=b3h, ghs2=adghjs, h2s2=adhjmn, is2=gs2, js2=gjs, hks2=dhjkl, k2s2=bdks2, ls2=ags2, ms2=dfgjs, bns2=dehl2, gns2=adgjns, n2s2=e2n2, os2=agjs, hps2=adhjkl, kps2=ajklm, p2s2=jklm, qs2=e3g2, rs2=adfgjs, bs3=bdel2, gs3=adgjs, hs3=adghjs, ks3=adjks, ns3=adgjns, ps3=adjps, s4=adgjs, b3t=b3h, b2ct=b2t, be2t=b3h, e3t=de2gh, cft=abct, bf2t=b3h, ef2t=b3h, b2gt=b2t, e2gt=e2t, bfgt=ab2t, beg2t=begt, g3t=g2t, b2ht=b2h2, cht=b2h2, beht=b2h2, e2ht=b2h2, fht=ab3h2, bght=b3h2, h2t=gh3, eit=eg2t, hit=g2ht, f2jt=ab3h, g2jt=gjt, ijt=gjt, fj2t=dfhjl, gj2t=j2t, hj2t=b2h2, j3t=dhj2l, bekt=b2kt, bfkt=ab2kt, efkt=ab2kt, f3kt=ab3h, bcgkt=bgkt, bg2kt=bgkt, eg2kt=egkt, bhkt=bh2k, ehkt=bh2k, ghkt=aefh2, ikt=gkt, fjkt=b2kt, hjkt=abh2k, bk2t=b3h, ek2t=b3h, fgk2t=dhk2l, g2k2t=b2kt, hk2t=bdh2k, jk2t=ab3h, k3t=ahk2l, e2flt=adg2jk2n, f2lt=df3t, beglt=ab2kt, bhlt=ab3h2, ehlt=defh2, hjlt=adefh2, bcklt=bklt, bgklt=ab3h, fgklt=af3t, hklt=abdh2k, j2klt=adghjkl, k2lt=dfk2t, bel2t=b2h, bfl2t=hk2l, efgl2t=hk2l, g2l2t=aghl3, ghl2t=bdh2k, jl2t=dhj2l, bkl2t=b3h, ekl2t=adhk2l, fkl2t=dhk2l, gkl2t=ahkl3, l3t=agl2t, bmt=b2t, cmt=bcgt, emt=begt, f2mt=b3h, fgmt=fmt, g2mt=gmt, hmt=b3h2, gjmt=jmt, j2mt=ghjkl, fkmt=ab2kt, gkmt=kmt, jkmt=ab2kt, flmt=ag2jk2n, jlmt=j2kt, klmt=dg2jk2n, l2mt=hl2m, m2t=b2t, b2nt=b3h2, cnt=b3h2, bent=adhjkn, e2nt=e2hn, bfnt=ab3h2, efnt=defh2, f2nt=b3h2, eg2nt=egnt, fg2nt=fgnt, bhnt=ab2h2, ehnt=efh2, ghnt=gh2n, hjnt=h2jn, j2nt=hj2n, bknt=bdh2k, eknt=ahjkn, fknt=ab2h2, hknt=ab3h2, gjknt=afh2j, k2nt=bh2k, elnt=adegkn2, flnt=dfghjn, glnt=ghln, hlnt=bh2k, jklnt=bdh2k, l2nt=aghln, fmnt=ab3h2, jmnt=defh2, kmnt=b2h2, lmnt=abghn, en2t=ehn2, fn2t=dhn2p, g2n2t=ghn2, hn2t=abehn2, gjn2t=ghjn2, kn2t=bdn2t, ln2t=agn2t, mn2t=bgn2t, gn3t=aehn2, b2ot=b3h, beot=b3h, ceot=bcden, e2ot=de2gh, bfot=ab3h, efot=e2ft, f3ot=g2jk2n, got=ot, bhot=b2h2, ehot=b2h2, j2ot=adhj2l, bkot=abfh, ckot=cdhk, f2kot=adg2jk2n, hkot=b3h2, k2ot=b3h, blot=ab2kt, hlot=defh2, fjlot=dfhjl, eklot=g2jk2n, fklot=ag2jk2n, l2ot=adhj2l, fmot=ab3h, jmot=aghjkl, kmot=abfh, lmot=aj2kt, bnot=adefh2, enot=e2hn, hnot=fh2o, knot=afh2o, lnot=adhj2n, mnot=dfh2j, bo2t=b2cn, co2t=bcgn, eo2t=bdeno, f2o2t=def2h, fko2t=bdfh, flo2t=adfhjl, klo2t=adghjkl, bcpt=bpt, bept=ab2h, e2pt=g2jk2n, bfpt=b2h, efpt=b2h, f2pt=ab2h, bgpt=ab2dkt, g2pt=gpt, hpt=efh2, j2pt=fhjl, kpt=adfgpt, blpt=abklt, eglpt=adg2jk2n, fglpt=f3t, gjlpt=dfhjl, el2pt=dhk2l, fl2pt=b3h, gl2pt=ahl3p, mpt=ab2dkt, bnpt=ab2h2, enpt=efh2, gjnpt=jnpt, lnpt=aghnp, n2pt=hn2p, bopt=ab2h, copt=ab2dkt, eopt=g2jk2n, fopt=adeghp, nopt=ajnpt, o2pt=fhl2o, p2t=adf3t, eqt=ae2lt, gqt=aeglt, iqt=aeg2lt, bkqt=b2h, hkqt=b3h2, k2qt=b3h, blqt=hk2l, flqt=aefl2t, hlqt=abh2k, klqt=dhk2l, mqt=b2kt, nqt=adehn2, oqt=aelot, pqt=aehlp, q2t=degl2t, brt=ab2h, crt=bclt, f2rt=dg2jk2n, egrt=ert, fgrt=frt, g2rt=grt, hrt=ab3h2, gjrt=jrt, ekrt=ab2h, fkrt=ag2jk2n, jkrt=b2h, k2rt=ab3h, elrt=ag2jk2n, flrt=g2jk2n, klrt=adg2jk2n, l2rt=dfhjl, mrt=ab2h, enrt=defh2, fnrt=b3h2, jnrt=fgjnt, knrt=ab2h2, n2rt=dhn2p, eort=ab3h, fort=ef2h, jort=fjot, kort=g2jk2n, lort=afhjl, nort=fnot, fprt=ab2h, gprt=aeghp, lprt=dg2jk2n, oprt=def2h, qrt=g2jk2n, er2t=b3h, fr2t=dg2jk2n, gr2t=r2t, kr2t=ag2jk2n, lr2t=g2jk2n, or2t=b3h, pr2t=ab2h, r3t=ab3h, f2st=b2h, bgst=b3h, fgst=fghs, hst=h2s, fjst=dhjkl, gjst=ghjs, bkst=b3h, ekst=b3h, jkst=aghjkl, k2st=b2h, lst=hls, mst=hjkl, bnst=adhjmn, fnst=fhns, gnst=ghns, jnst=admn2s, n2st=adegkn2, ost=aghjs, pst=klmn, qst=de2gh, rst=ahjkl, bs2t=b3h, gs2t=adghjs, ks2t=dghjkl, ns2t=mn2s, s3t=adghjs, bt2=bh2, ct2=b2h2, et2=eh2, f2t2=b2h2, fgt2=ft2, g2t2=gt2, ght2=ht2, it2=gt2, fjt2=aefh2, gjt2=jt2, hjt2=adefh2, j2t2=b2h2, fkt2=ab3h2, gkt2=adft2, hkt2=ab2h2, jkt2=defh2, k2t2=bdh2k, flt2=b3h2, glt2=g2hlt, hlt2=b2h2, jlt2=adefh2, klt2=abdh2k, l2t2=bdh2k, mt2=adefh2, fnt2=b2h2, gnt2=gh2n, hnt2=b3h2, jnt2=fh2j, knt2=ab3h2, lnt2=b3h2, n2t2=abehn2, fot2=ab2h2, hot2=ab3h2, kot2=b3h2, lot2=defh2, not2=fh2o, pt2=efh2, qt2=adefh2, rt2=defh2, fst2=ab3h2, gst2=gh2s, jst2=ab3h2, kst2=b2h2, nst2=defh2, s2t2=b2h2, t3=ht2>

P = {a, b2, b4, c, b2c, ad, bcd, ae, bce, ade, cde, ae2, ade2, ae3, ade3, bf, abcf, df, acdf, ef, acef, af2, adef2, df3, ag, b2g, cg, adg, bcdg, aeg, adeg, cdeg, ae2g, ade2g, ae3g, ade3g, bfg, dfg, acdfg, efg, ag2, adg2, aeg2, adeg2, ae2g2, ade2g2, ae3g2, ade3g2, dfg2, efg2, ag3, adg3, aeg3, adeg3, bh, ab3h, ach, dh, eh, abdeh, afh, cdfh, adefh, df2h, af3h, bgh, dgh, egh, afgh, dg2h, dg3h, b2h2, adh2, adeh2, adgh2, ah3, agh3, ai, ci, adi, aei, adei, dfi, dhi, j, dj, afj, df2j, gj, dgj, afgj, g2j, dg2j, ahj, dfhj, aghj, dfghj, dh2j, dgh2j, ij, dij, aj2, adj2, dfj2, agj2, adgj2, ag2j2, adg2j2, dhj2, afhj2, dghj2, j3, dj3, gj3, dgj3, g2j3, dg2j3, ahj3, ak, b2k, ck, b2ck, adk, bcdk, aek, ade2k, ae3k, dfk, agk, b2gk, cgk, adgk, bcdgk, aegk, dfgk, ag2k, adg2k, aeg2k, dfg2k, ag3k, adg3k, aeg3k, achk, dhk, dghk, dg2hk, dg3hk, adh2k, aik, adik, aeik, jk, gjk, g2jk, ijk, adj2k, j3k, ak2, adk2, aek2, ade2k2, ae3k2, agk2, adgk2, ag2k2, adg2k2, ag3k2, adg3k2, aik2, adik2, jk2, adk3, l, acl, dl, abcdl, el, del, acdel, e2l, de2l, adfl, aefl, f2l, gl, acgl, dgl, abcdgl, egl, degl, adfgl, aefgl, g2l, dg2l, eg2l, deg2l, adfg2l, aefg2l, adhl, aehl, fhl, adghl, aeghl, adg2hl, dh2l, il, dil, ajl, adjl, fjl, agjl, adgjl, hjl, ghjl, j2l, dj2l, adfj2l, adhj2l, aj3l, adj3l, kl, ackl, dkl, abcdkl, ekl, gkl, dgkl, egkl, g2kl, dg2kl, ajkl, agjkl, dk2l, al2, adl2, ael2, adel2, abfl2, dfl2, af2l2, agl2, adgl2, aegl2, adegl2, dfgl2, ag2l2, adg2l2, dfg2l2, abhl2, dhl2, afhl2, dghl2, dg2hl2, jl2, djl2, adkl2, aekl2, adgkl2, jkl2, l3, dl3, adfl3, gl3, dgl3, adhl3, adghl3, dkl3, am, bcm, adm, cdm, aem, bdem, fm, acfm, adf2m, agm, adgm, aegm, fgm, ag2m, adg2m, hm, ghm, jm, gjm, adhjm, adghjm, adj2m, akm, agkm, ag2km, lm, dlm, elm, aflm, ajlm, dj2lm, adl2m, fl2m, dl3m, am2, agm2, djm2, n, ab2n, ab2cn, dn, acdn, en, acen, den, e2n, de2n, e3n, de3n, bfn, adfn, gn, dgn, acdgn, egn, degn, e2gn, de2gn, e3gn, de3gn, adfgn, g2n, dg2n, eg2n, deg2n, adfg2n, g3n, dg3n, eg3n, deg3n, ahn, bdehn, afhn, bghn, afghn, ajn, adjn, fjn, agjn, adgjn, fgjn, ag2jn, adg2jn, dfhjn, dfghjn, j2n, dj2n, adfj2n, gj2n, dgj2n, aj3n, adj3n, agj3n, adgj3n, abkn, dkn, acdkn, abgkn, dgkn, abg2kn, dg2kn, abg3kn, dg3kn, ahkn, ajkn, agjkn, ag2jkn, k2n, dk2n, gk2n, dgk2n, dg2k2n, aln, adln, cdln, aeln, adeln, ae2ln, ade2ln, dfln, agln, adgln, aegln, adegln, jln, djln, afjln, gjln, dgjln, aj2ln, adj2ln, adkln, aekln, adgkln, jkln, l2n, dl2n, dkl2n, mn, acmn, dmn, emn, dgmn, dg2mn, ajmn, agjmn, adhjmn, dj2mn, kmn, adlmn, jlmn, dl2mn, an2, b2n2, adn2, aen2, aden2, ae2n2, ade2n2, abfn2, dfn2, agn2, adgn2, aegn2, adegn2, dfgn2, ag2n2, adg2n2, dhn2, ehn2, dghn2, jn2, djn2, gjn2, dgjn2, g2jn2, dg2jn2, ahjn2, abkn2, adkn2, aekn2, fkn2, abgkn2, adgkn2, aegkn2, adg2kn2, jkn2, gjkn2, ak2n2, adk2n2, ln2, dln2, dkln2, bmn2, admn2, adgmn2, jmn2, akmn2, n3, dn3, en3, den3, gn3, dgn3, ahn3, kn3, dekn3, dmn3, ao, bco, ado, b2do, cdo, aeo, ceo, adeo, bcdeo, ae2o, ade2o, fo, acfo, bdfo, abcdfo, defo, acdefo, adf2o, aef2o, f3o, ago, adgo, aego, adego, ae2go, ade2go, fgo, ho, bdho, deho, adfho, aefho, adh3o, jo, djo, adfjo, gjo, dgjo, adhjo, aj2o, adj2o, agj2o, adgj2o, ako, bcko, adko, b2dko, cdko, fko, agko, adgko, fgko, hko, adk2o, adgk2o, lo, abclo, dlo, acdlo, elo, delo, e2lo, de2lo, aflo, adeflo, df2lo, glo, dglo, ahlo, adehlo, dfhlo, ajlo, adjlo, dfjlo, dhjlo, j2lo, dj2lo, klo, dklo, gklo, dgklo, al2o, adl2o, fl2o, adf2l2o, hl2o, adfhl2o, amo, dfmo, dhmo, djmo, lmo, adjlmo, adm2o, no, dno, eno, deno, afno, gno, dgno, afgno, ajno, adjno, kno, abdkno, gkno, dk2no, alno, adlno, aglno, adglno, mno, adjmno, almno, ao2, co2, ado2, bcdo2, aeo2, adeo2, bfo2, dfo2, acdfo2, efo2, af2o2, adef2o2, df3o2, dho2, ako2, bdko2, dfko2, dhko2, ak2o2, lo2, aclo2, dlo2, abcdlo2, elo2, delo2, adflo2, aeflo2, f2lo2, adhlo2, klo2, admo2, dlmo2, no2, dno2, p, acp, dp, abcdp, ep, dep, de2p, e3p, bfp, adfp, f2p, gp, acgp, dgp, abcdgp, egp, degp, adfgp, g2p, dg2p, adhp, fhp, adghp, ajp, adjp, agjp, adgjp, hjp, ghjp, j2p, dj2p, gj2p, adhj2p, aj3p, adj3p, hj3p, dkp, ekp, dgkp, dg2kp, ajkp, dk2p, alp, adlp, aelp, adelp, dflp, aglp, adglp, aeglp, adeglp, dfglp, dhlp, dghlp, jlp, djlp, gjlp, dgjlp, adklp, l2p, dl2p, el2p, adfl2p, gl2p, dgl2p, adhl2p, adghl2p, ajl2p, adjl2p, al3p, adl3p, dmp, adlmp, dl2mp, adnp, aenp, adgnp, adg2np, jnp, djnp, dgjnp, adknp, lnp, dlnp, al2np, adl2np, n2p, dn2p, gn2p, dgn2p, adjn2p, op, dop, acdop, eop, afop, bdfop, df2op, ahop, dfhop, alop, adlop, aelop, flop, hlop, dl2op, afl2op, o2p, bdo2p, deo2p, adfo2p, f2o2p, ko2p, alo2p, dflo2p, ap2, adp2, aep2, dfp2, agp2, adgp2, dhp2, jp2, djp2, dgjp2, adkp2, lp2, dlp2, glp2, admp2, dnp2, adop2, fop2, ao2p2, p3, dp3, aq, adq, aeq, adeq, ae2q, ade2q, ae3q, ade3q, fq, agq, adgq, aegq, adegq, fgq, ag2q, adg2q, fg2q, hq, ghq, adh2q, aiq, adiq, akq, adekq, ae2kq, ade3kq, agkq, ag2kq, aikq, ak2q, adek2q, ak3q, lq, dlq, glq, dglq, g2lq, dg2lq, klq, amq, nq, dnq, gnq, dgnq, knq, an2q, adn2q, akn2q, aoq, adoq, dfoq, agoq, adgoq, dhoq, loq, dloq, ao2q, ado2q, fo2q, lo2q, dlo2q, pq, dpq, depq, e2pq, gpq, dgpq, kpq, alpq, adlpq, adglpq, anpq, opq, do2pq, ap2q, aq2, adq2, aeq2, adeq2, ae2q2, ade2q2, agq2, adgq2, adkq2, adk2q2, dpq2, aq3, adq3, r, abcr, dr, acdr, er, acer, afr, df2r, gr, dgr, acdgr, egr, afgr, g2r, dg2r, eg2r, ahr, aghr, ajr, agjr, kr, dkr, gkr, dgkr, g2kr, dg2kr, alr, adlr, aelr, flr, hlr, dl2r, mr, gmr, bnr, adnr, bgnr, adgnr, adg2nr, ahnr, jnr, gjnr, dn2r, kn2r, or, acor, bdor, deor, acdeor, adfor, f2or, adhor, adjor, kor, alor, adelor, dflor, dhlor, l2or, anor, abo2r, do2r, acdo2r, afo2r, dko2r, aeko2r, adlo2r, flo2r, adpr, fpr, adgpr, dlpr, aopr, dfopr, lopr, ado2pr, qr, gqr, doqr, ar2, ader2, dfr2, agr2, dhr2, lr2, adflr2, adhlr2, al2r2, ador2, afkor2, ahkor2, adklor2, ao2r2, aklo2r2, pr2, dopr2, o2pr2, dr3, as, cs, ads, aes, ades, dfs, ags, adgs, dfgs, abhs, dhs, dghs, gh2s, ais, cis, adis, js, djs, afjs, gjs, dgjs, afgjs, ahjs, aghjs, adks, aeks, adgks, jks, adk2s, ls, dls, adhls, dkls, adms, ns, dns, adfns, gns, dgns, adfgns, adhns, adghns, ajns, adjns, fjns, agjns, adgjns, hjns, dkns, dgkns, alns, adlns, adklns, dmns, an2s, adn2s, dhn2s, adkn2s, admn2s, aos, ados, fos, nos, dnos, ao2s, ado2s, dfo2s, ps, dps, gps, dgps, ajps, adjps, dkps, anps, adnps, agnps, adgnps, adp2s, aqs, adqs, drs, dgrs, ors, do2rs, as2, ads2, ags2, adgs2, dhs2, adks2, adgks2, ns2, dns2, adhns2, dkns2, ps2, dps2, gps2, dgps2, anps2, adnps2, as3, ads3, t, act, dt, ab2dt, et, det, acdet, de2t, aft, bdft, df2t, gt, acgt, dgt, egt, degt, acdegt, afgt, g2t, dg2t, eg2t, deg2t, afg2t, adht, it, acit, dit, afit, ajt, adjt, agjt, adgjt, dj2t, kt, ackt, abdkt, abcdkt, gkt, acgkt, abdgkt, g2kt, adhkt, dk2t, dgk2t, alt, clt, adlt, aelt, adelt, cdelt, ade2lt, flt, abdflt, aglt, cglt, adglt, aeglt, adeglt, fglt, ag2lt, adg2lt, aeg2lt, adeg2lt, fg2lt, ailt, adilt, jlt, djlt, gjlt, dgjlt, adj2lt, aklt, cklt, bl2t, dl2t, el2t, dgl2t, egl2t, dkl2t, mt, gmt, almt, ant, adnt, aent, adent, agnt, adgnt, aegnt, adegnt, ag2nt, adg2nt, jnt, djnt, gjnt, dgjnt, aknt, lnt, adjlnt, n2t, dn2t, dgn2t, ajn2t, an3t, adn3t, ot, dot, acdot, deot, adfot, f2ot, adjot, ahjot, alot, adlot, cdlot, adelot, dflot, djlot, anot, adnot, djnot, do2t, afo2t, adlo2t, adno2t, apt, cpt, agpt, cgpt, dlpt, dglpt, aopt, lopt, qt, dqt, alqt, adlqt, art, dfrt, agrt, lrt, adort, dr2t, st, acst, dst, est, dgst, dist, ajst, adnst, ds2t, adt2, adgt2, aht2, djt2, adkt2, dlt2, ajot2, o2t2}

Phi = 1 a b c d a e f g h i j k l m n o p q r s t

Monoid Structure

Idempotent  |G|  |Arch|
144
b442608
c44
de3412
cg48
de3g24180
g3416
b2h2 *43056
adj3412
adg2j3444
de3k2452
dj3l444
agl3436
e2n24224
adn3412
o2412
co248
adgjs444