Certificate for #4297 ⟨a, b | abababaab=ba

Completion settings:

[1] abababaab=ba

Axiom: abababaab=ba.

Referenced by [4], [5], [6], [8], [18].

[2] abaabab=c

Axiom: abaabab=c.

Referenced by [3], [4], [5], [6], [7], [9], [10], [11], [14], [19].

[3] abaabc=caabab

Overlap of [2] abaabab=c with [2] abaabab=c:

abaab ab abaabab

Critical pair: abaabc=caabab.

Referenced by [9], [18].

[4] ababc=baab

Overlap of [1] abababaab=ba with [2] abaabab=c:

abab abaab abaabab

Critical pair: ababc=baab.

Referenced by [7], [8], [9], [15], [18].

[5] ababa=cabaab

Overlap of [2] abaabab=c with [1] abababaab=ba:

aba abab abababaab

Critical pair: ababa=cabaab.

Referenced by [6].

[6] abaabba=ccc

Overlap of [2] abaabab=c with [1] abababaab=ba:

abaab ab abababaab

Critical pair: abaabba=cababaab.

Reduce RHS:

[5]c(ababa)ab
[2]cc(abaabab)
ccc

Referenced by [7], [8], [12], [16].

[7] cabc=cccab

Overlap of [2] abaabab=c with [4] ababc=baab:

abaab ab ababc

Critical pair: abaabbaab=cabc.

Reduce LHS:

[6](abaabba)ab
cccab

Flip LHS and RHS.

Referenced by [13], [20], [22].

[8] baba=baabcc

Overlap of [1] abababaab=ba with [6] abaabba=ccc:

abab abaab abaabba

Critical pair: ababccc=baba.

Reduce LHS:

[4](ababc)cc
baabcc

Flip LHS and RHS.

Referenced by [9], [10], [18].

[9] abacabaab=ca

Overlap of [2] abaabab=c with [8] baba=baabcc:

abaa bab baba

Critical pair: abaabaabcc=ca.

Reduce LHS:

[3]aba(abaabc)c
[4]abaca(ababc)
abacabaab

Referenced by [11], [12], [20].

[10] baabccabab=bc

Overlap of [8] baba=baabcc with [2] abaabab=c:

b aba abaabab

Critical pair: bc=baabccabab.

Flip LHS and RHS.

Referenced by [21].

[11] abacc=caab

Overlap of [9] abacabaab=ca with [2] abaabab=c:

abac abaab abaabab

Critical pair: abacc=caab.

Referenced by [12], [17].

[12] caba=caabcc

Overlap of [9] abacabaab=ca with [6] abaabba=ccc:

abac abaab abaabba

Critical pair: abacccc=caba.

Reduce LHS:

[11](abacc)cc
caabcc

Flip LHS and RHS.

Referenced by [13], [14], [15], [16], [17], [18], [19], [20], [21].

[13] cccaabccba=cccaabccccccab

Overlap of [7] cabc=cccab with [12] caba=caabcc:

cab c caba

Critical pair: cabcaabcc=cccababa.

Reduce LHS:

[7](cabc)aabcc
[12]cc(caba)abcc
[7]cccaabc(cabc)c
[7]cccaabccc(cabc)
cccaabccccccab

Reduce RHS:

[12]cc(caba)ba
cccaabccba

Flip LHS and RHS.

Referenced by [19], [20], [21].

[14] caabccaabccb=cc

Overlap of [12] caba=caabcc with [2] abaabab=c:

c aba abaabab

Critical pair: cc=caabccabab.

Reduce RHS:

[12]caabc(caba)b
caabccaabccb

Flip LHS and RHS.

Referenced by [20].

[15] caabccbc=cbaab

Overlap of [12] caba=caabcc with [4] ababc=baab:

c aba ababc

Critical pair: cbaab=caabccbc.

Flip LHS and RHS.

Referenced by [21].

[16] caabccabba=cccc

Overlap of [12] caba=caabcc with [6] abaabba=ccc:

c aba abaabba

Critical pair: cccc=caabccabba.

Flip LHS and RHS.

Referenced by [18], [21].

[17] caabcccc=ccaab

Overlap of [12] caba=caabcc with [11] abacc=caab:

c aba abacc

Critical pair: ccaab=caabcccc.

Flip LHS and RHS.

Referenced by [19], [20], [21].

[18] ba=ccccab

Overlap of [1] abababaab=ba with [8] baba=baabcc:

a bababaab baba

Critical pair: abaabccbaab=ba.

Reduce LHS:

[3](abaabc)cbaab
[4]ca(ababc)baab
[12](caba)abbaab
[16](caabccabba)ab
ccccab

Flip LHS and RHS.

Defines rule #3.

Referenced by [19], [20], [21], [22].

[19] acccccaabccabb=c

Overlap of [2] abaabab=c with [18] ba=ccccab:

a baabab ba

Critical pair: accccababab=c.

Reduce LHS:

[12]accc(caba)bab
[13]ac(cccaabccba)b
[17]accc(caabcccc)ccabb
acccccaabccabb

Referenced by [22].

[20] acccccccc=ca

Overlap of [9] abacabaab=ca with [18] ba=ccccab:

a bacabaab ba

Critical pair: accccabcabaab=ca.

Reduce LHS:

[7]accc(cabc)abaab
[12]accccc(caba)baab
[13]accc(cccaabccba)ab
[17]accccc(caabcccc)ccabab
[12]acccccccaabc(caba)b
[14]acccccc(caabccaabccb)
acccccccc

Defines rule #1.

Referenced by [22].

[21] bc=ccccccccccccccccb

Overlap of [10] baabccabab=bc with [18] ba=ccccab:

baabccabab ba

Critical pair: ccccababccabab=bc.

Reduce LHS:

[12]ccc(caba)bccabab
[15]ccc(caabccbc)cabab
[18]cccc(ba)abcabab
[12]ccccccc(caba)bcabab
[15]ccccccc(caabccbc)abab
[18]cccccccc(ba)ababab
[12]ccccccccccc(caba)babab
[13]ccccccccc(cccaabccba)bab
[17]ccccccccccc(caabcccc)ccabbab
[16]cccccccccccc(caabccabba)b
ccccccccccccccccb

Flip LHS and RHS.

Defines rule #2.

Referenced by [22].

[22] acccccaccccaccccabbb=c

Simplify [19] acccccaabccabb=c.

Reduce LHS:

[21]acccccaa(bc)cabb
[20]accccca(acccccccc)ccccccccbcabb
[20]acccccac(acccccccc)bcabb
[7]acccccac(cabc)abb
[18]acccccacccca(ba)bb
acccccaccccaccccabbb

Defines rule #4.