Details Page for 0.0702

Complete Solution is Known:

MSV File: q-0.0702.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₄₃₇(0.0702):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t | a²=1, b³=b, b²c²=c², c⁴=c², b²cd=cd, c²d=ac², d²=c², be=c², c²e=bc², de=abc², e⁴=e², cf=c², b²df=df, f²=c², b²g=g, cg=c², dg=ac³, eg=bc³, fg=c², g²=c², b²ch=ch, c²h=bc³, dh=abc³, ceh=c², e²h=e³f, b²fh=fh, efh=c², gh=bc², bh³=bh, ch³=ch, fh³=fh, h⁴=h², bi=c³, ci=bc², e³i=ei, fi=bc², gi=bc², hi=c², i²=c², bj=c², c²j=bc², dj=abc², ce²j=bc³, e²fj=bc³, gj=bc³, hj=efj, eij=bc³, j²=e³j, c²k=ac², b²dk=dk, dfk=acd, efk=ace, fhk=ach, dik=bc³, cejk=aij, e²jk=abc², fjk=acj, ik²=aik, cdk³=acdk², cek³=acek², fk³=ck³, gk³=agk², chk³=achk², cjk³=acjk², ck⁴=ack³, dk⁴=adk³, ek⁴=aek³, hk⁴=ahk³, jk⁴=ajk³, k⁵=ak⁴, b²cl=cl, c²l=ac³, dl=c³, el=ae³f, b²fl=fl, gl=ac², b²hl=hl, ch²l=cl, fh²l=fl, h³l=hl, il=abc², jl=abc³, fkl=acl, ck³l=ack²l, k⁴l=ak³l, l²=c², bm=bh²l, c²m=ac³, dm=c³, gm=ac², chm=chl, fhm=fhl, e²jm=abc³, fkm=acm, ck³m=ack²m, k⁴m=ak³m, lm=ae²fm, m²=c², b²n=n, c²n=bc³, en=c³, hn=c², in=c², jn=c³, k⁴n=ak³n, ln=acdkn, mn=abc², n²=c², b²co=co, c³o=co, b²do=do, cdo=aco, ceo=bco, e³o=eo, fo=co, go=co, bho=co, cho=bc²o, eho=co, h³o=ho, io=bco, jo=bc²o, cko=aco, bk²o=abko, dk²o=adko, k⁴o=ak³o, lo=aco, cmo=ac²o, no=bco, o²=c², bp=c³, cp=acjm, dp=abc³, fp=afjm, gp=bc², hp=aefjm, ip=aijm, jp=c³, e²k²p=e²i, k⁴p=ak³p, lp=abc², e²mp=mp, k²mp=e²im, np=c², op=bco, p²=c², b²q=q, cq=bc³, dq=acdkn, eq=c², fq=bc³, gq=bc³, hq=c³, iq=c³, jq=c², k²q=akq, lq=abc³, mq=abc³, nq=c³, oq=bc²o, pq=c³, q²=c², b²r=r, cr=bc³, dr=dfn, er=c², fr=bc³, gr=bc³, hr=c³, ir=c³, jr=c², kr=acn, lr=abc³, mr=abc³, nr=c³, or=bc²o, pr=c³, qr=c², r²=c², b²s=s, c²s=s, ds=as, es=bs, fs=cs, gs=cs, hs=bcs, is=bcs, js=bs, ks=as, ls=acs, ms=acs, ns=bcs, ps=bcs, qs=bs, rs=bs, s²=c², b²t=t, c²t=t, dt=at, et=bt, ft=ct, gt=ct, ht=bct, it=bct, jt=bt, kt=at, lt=act, mt=act, nt=bct, pt=bct, qt=bt, rt=bt, t²=c²>

P = {a, ab, ab², c², e, ae², e³, abh, bch, bfh, ah², ab²h², adi, j, aej, ae³j, k, bk, b²k, aek, ae³k, h²k, b²h²k, ajk, ak², abk², ab²k², ek², e³k², abchk², ah²k², ab²h²k², jk², k³, bk³, b²k³, aek³, ae³k³, h²k³, b²h²k³, ajk³, ak⁴, abk⁴, ab²k⁴, acl, afl, ckl, acm, ace²m, afm, ae²fm, aehm, aeh³m, aeim, acejm, aefjm, aijm, ckm, ce²km, ehkm, eh³km, acek²m, ace³k²m, aehk²m, aeh³k²m, acjk²m, hk³m, h³k³m, bcn, abcdn, bfn, abdfn, bgn, abckn, bcdkn, ack²n, abfk²n, abgk²n, ck³n, bck³n, abko, bdko, k³mo, e²k³mo, h²k³mo, aemp, ekmp, bq, br}

Phi = 1 1 a a ack ack ck ck a c² b b ck c³ c d ac² c² e f g h i j k ac² c³ c³ ac³ aef ac² ac² bc² l m n c³ ac² ae³j c² bc² o ace³k p abc³ q ac² ac² abc² c³ ac³ abc³ ac²o abc² r ac³ abc³ c³ c³ ac² ac²o c² bc² c²o ac² bc³ abc³ afjm bc² ac² c³ c³ bc³ ac³ bc²o abc² bc² bc² abc³ bc³ c³ c²o ac²o c² bc² aco ac² bc³ c²o bc² bc² ac² aco c³ ac³ ac³ c²o c²o ac² ac² abc³ bc³ c³ c²o ac²o c² bc² co ac² c³ c³ bc² bc² ac² aco c³ ac³ ac³ ac²o c²o ac² ac² aco c³ c³ bc³ ac²o c² bc² co co c³ c³ c²o c²o abc² ac² co ac³ ac³ c³ c²o bc² bc² co bco bc³ bc³ ac²o abc²o bc² aco aco c³ abc³ bc³ c²o abc² aco co ac³ bco c³ ac² ac² bc² bc² aco bc³ bc³ ac²o abc³ abc²o bco aco ac²o abc³ ac³ bc² ac² aco abco co abc³ abc³ abc²o abc²o bc² bc² aco bc³ bc³ bc²o abc³ bc² abco bco bco s abc²o bc² as cs bco co abc³ abc³ c³ cs as bco acs bc³ c²o bc²o ac²o bc² bs bco aco abc³ abc²o bc² abc² cs abco co acs abs ac³ c²o bco abc³ aco bc³ as bc²o ac²o bc² os bco aco cs c²o c²o abc² abs abco co bco aos c²o c²o acs s aco aco c²o acs ac²o s as aco aco cs os c²o c²o abs s co bco os ac²o c²o bcs s aco ac² os acs ac²o c²o cos c³ aco abco c²o ac²o bc²o as s co bco cs abc²o c²o c² bc² abcs ac² os bos ac²o c²o cos c³ aco abco os acs c²o abs acos co aco cs ac² bc² bs bs abco ac² bco bos ac²o c²o cos cos bco os os bc²o c³ ac² cos bco aco cs ac² bos ac²o acos abco bco bco aos abc²o c²o bs c³ aco ac² c² acs c²o abc²o cos bco aco ac² ac² abc²o c² bs abcs aco aco bos bc² c²o bs acos bc³ ac² c² bc²o c²o c²o bcos s aco ac² ac² abc²o c²o abcs abcs co aco bc² bc² c²o bcos as bc³ bc² abos os c²o c³ abcos abc³ aco abcs ac² bc² bc²o bcos s co aco bc² bc² abc²o bs c³ abs ac² abcs bc² c²o abc²o abcos abc³ aco abco ac² bc² abc²o abc²o s bs aco bc² bc² acs t bc³ bc³ bco aco bos bc²o cs abc³ cos bco bc² abos ac² abc²o abc³ t acos aco bc² cs acs t bcos s ac³ bs aco abcs ac² abc³ abc³ bco bc² abc² aco cs abcs c²o c³ bco bc² cs acs t t bcos bco ct ct abcs cs ac²o bco s ct abc² bc² cs abcs c²o abc³ as co co acs t bc³ as as ct ac² ac² cs ac²o ac³ s s abc² ac² bc² bc² c²o abc³ as co at acs cs bc³ abcos abc³ bs ac² t cs bcs ct s s abc² ac² bcs bc² bt bs bs bos c² bc² bcs t c³ abc³ as abt bct cs bcs aos abc³ s as ac² cs bc² abc³ act as abs bc² bc² cs cs c³ abc³ acos bc² ac² c²o bt at bc³ cot as acos cs bc² acs t as ct bc² abcs bcs t c³ abc³ abc³ bc² abt cs ot at bc³ bs s act ac² abt abcs t as act ct abcs bot acs t abc³ acos bcos bc² bcs bcs abcs abt abt as acot c² abcs acs c²o t abt ct ct ac² t bco abc³ abt abc²o ot ot bcs abcs cot cot as as abct abos bco abt t abc²o cos aot aot ac² bco cot ac³ abc²o c²o ot abc² abt os cot bcot abc²o ot ct bco cs t abc²o bcot c²o aot st t c³ s as as acos abc² aos aco bcot ast abc²o ct ct bco co ac³ abt c²o c²o aot act os co s abc³ as ac²o ot aos aco cot st abc²o ac²o abt bc² aco abcot cot c²o c²o bcos aot os co bos abc³ cot cst cs bst co abcs as acot ac²o bcos aot abos os cot acot bc² cst abct ot c³ bos cot abc² bc²o bct abt st bco cot abc²o cos bcos bct bos bos abc³ cot bs aot acos ot co abcs abt cot as bot bst abot os abcst acot bc²o ot aot bco aco abos t bc²o s acos ot os aos abt cot as st bco acs os os bcot abcst bs aot act os os abt bcos as as t aost co cot cot acos bcos aot abos aos os bcot cos ac² aot bc² os abos abcst s cos acos ot ot os aos t abs acos bct abc³ abos os acot bc²o cos c²o act os os abcot bc² cos as as ot abcs abcs cot t bc² bs bct bos aco bcs at abt cos abot abct abos bos acot cos c²o as ct acs aco cot abc²o bcos bs bs st os os abt t cos aot abct ast abcot bc² bc²o cst acos ot s aco cot t abcst abt ot ast bos bos

Monoid Structure