Certificate for #7544 ⟨a, b | aaa=1, babbbb=a

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #3.

Referenced by [4], [6], [9], [10], [11], [15], [16], [19], [21], [22], [36].

[2] babbbb=a

Axiom: babbbb=a.

Referenced by [3], [5], [7], [8], [11], [18], [21], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35].

[3] babbba=aabbbb

Overlap of [2] babbbb=a with [2] babbbb=a:

babbb b babbbb

Critical pair: babbba=aabbbb.

Referenced by [4], [5].

[4] aabbbbaa=babbb

Overlap of [3] babbba=aabbbb with [1] aaa=1:

babbb a aaa

Critical pair: babbb=aabbbbaa.

Flip LHS and RHS.

Referenced by [6].

[5] babba=aabbbbbbbb

Overlap of [3] babbba=aabbbb with [2] babbbb=a:

babb ba babbbb

Critical pair: babba=aabbbbbbbb.

Referenced by [15], [18].

[6] bbbbaa=ababbb

Overlap of [1] aaa=1 with [4] aabbbbaa=babbb:

a aa aabbbbaa

Critical pair: ababbb=bbbbaa.

Flip LHS and RHS.

Referenced by [7], [11].

[7] babababbb=abaa

Overlap of [2] babbbb=a with [6] bbbbaa=ababbb:

bab bbb bbbbaa

Critical pair: babababbb=abaa.

Referenced by [8].

[8] babaa=abaab

Overlap of [7] babababbb=abaa with [2] babbbb=a:

baba babbb babbbb

Critical pair: babaa=abaab.

Referenced by [9], [12], [14], [17].

[9] abaaba=bab

Overlap of [8] babaa=abaab with [1] aaa=1:

bab aa aaa

Critical pair: bab=abaaba.

Flip LHS and RHS.

Referenced by [10], [11], [12], [13].

[10] baaba=aabab

Overlap of [1] aaa=1 with [9] abaaba=bab:

aa a abaaba

Critical pair: aabab=baaba.

Flip LHS and RHS.

Referenced by [15].

[11] bbbbabab=aba

Overlap of [6] bbbbaa=ababbb with [9] abaaba=bab:

bbbba a abaaba

Critical pair: bbbbabab=ababbbbaaba.

Reduce RHS:

[2]a(babbbb)aaba
[1](aaa)aba
aba

Referenced by [21].

[12] abaabba=bbab

Overlap of [8] babaa=abaab with [9] abaaba=bab:

b abaa abaaba

Critical pair: bbab=abaabba.

Flip LHS and RHS.

Referenced by [14].

[13] bababa=ababab

Overlap of [9] abaaba=bab with [9] abaaba=bab:

aba aba abaaba

Critical pair: ababab=bababa.

Flip LHS and RHS.

Referenced by [15].

[14] abaabbba=bbbab

Overlap of [8] babaa=abaab with [12] abaabba=bbab:

b abaa abaabba

Critical pair: bbbab=abaabbba.

Flip LHS and RHS.

Referenced by [16], [17].

[15] bbabab=abbbbbbbbba

Overlap of [10] baaba=aabab with [13] bababa=ababab:

baa ba bababa

Critical pair: baaababab=aababbaba.

Reduce LHS:

[1]b(aaa)babab
bbabab

Reduce RHS:

[5]aa(babba)ba
[1](aaa)abbbbbbbbba
abbbbbbbbba

Referenced by [20].

[16] baabbba=aabbbab

Overlap of [1] aaa=1 with [14] abaabbba=bbbab:

aa a abaabbba

Critical pair: aabbbab=baabbba.

Flip LHS and RHS.

Referenced by [21].

[17] abaabbbba=bbbbab

Overlap of [8] babaa=abaab with [14] abaabbba=bbbab:

b abaa abaabbba

Critical pair: bbbbab=abaabbbba.

Flip LHS and RHS.

Referenced by [19].

[18] baba=aabbbbbbbbbbbb

Overlap of [5] babba=aabbbbbbbb with [2] babbbb=a:

bab ba babbbb

Critical pair: baba=aabbbbbbbbbbbb.

Referenced by [20].

[19] baabbbba=aabbbbab

Overlap of [1] aaa=1 with [17] abaabbbba=bbbbab:

aa a abaabbbba

Critical pair: aabbbbab=baabbbba.

Flip LHS and RHS.

Referenced by [21].

[20] baabbbbbbbbbbbbb=abbbbbbbbba

Simplify [15] bbabab=abbbbbbbbba.

Reduce LHS:

[18]b(baba)b
baabbbbbbbbbbbbb

Referenced by [21].

[21] baab=abbbbbbbbbbbba

Overlap of [20] baabbbbbbbbbbbbb=abbbbbbbbba with [16] baabbba=aabbbab:

baabbbbbbbbbbbb b baabbba

Critical pair: baabbbbbbbbbbbbaabbbab=abbbbbbbbbaaabbba.

Reduce LHS:

[16]baabbbbbbbbbbb(baabbba)b
[16]baabbbbbbbbbb(baabbba)bb
[16]baabbbbbbbbb(baabbba)bbb
[16]baabbbbbbbb(baabbba)bbbb
[16]baabbbbbbb(baabbba)bbbbb
[16]baabbbbbb(baabbba)bbbbbb
[16]baabbbbb(baabbba)bbbbbbb
[16]baabbbb(baabbba)bbbbbbbb
[19](baabbbba)abbbabbbbbbbbb
[11]aa(bbbbabab)bbabbbbbbbbb
[1](aaa)babbabbbbbbbbb
[2]bab(babbbb)bbbbb
[2]ba(babbbb)b
baab

Reduce RHS:

[1]abbbbbbbbb(aaa)bbba
abbbbbbbbbbbba

Referenced by [22].

[22] bbbbbbbbbbbbba=abbbbbbbbbbbbb

Overlap of [21] baab=abbbbbbbbbbbba with [21] baab=abbbbbbbbbbbba:

baa b baab

Critical pair: baaabbbbbbbbbbbba=abbbbbbbbbbbbaaab.

Reduce LHS:

[1]b(aaa)bbbbbbbbbbbba
bbbbbbbbbbbbba

Reduce RHS:

[1]abbbbbbbbbbbb(aaa)b
abbbbbbbbbbbbb

Referenced by [23].

[23] bbbbbbbbbbbba=abbbbbbbbbbbbbbbbb

Overlap of [22] bbbbbbbbbbbbba=abbbbbbbbbbbbb with [2] babbbb=a:

bbbbbbbbbbbb ba babbbb

Critical pair: bbbbbbbbbbbba=abbbbbbbbbbbbbbbbb.

Referenced by [24].

[24] bbbbbbbbbbba=abbbbbbbbbbbbbbbbbbbbb

Overlap of [23] bbbbbbbbbbbba=abbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbbbbbbbbbb ba babbbb

Critical pair: bbbbbbbbbbba=abbbbbbbbbbbbbbbbbbbbb.

Referenced by [25].

[25] bbbbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [24] bbbbbbbbbbba=abbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbbbbbbbbb ba babbbb

Critical pair: bbbbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [26].

[26] bbbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [25] bbbbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbbbbbbbb ba babbbb

Critical pair: bbbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [27].

[27] bbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [26] bbbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbbbbbbb ba babbbb

Critical pair: bbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [28].

[28] bbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [27] bbbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbbbbbb ba babbbb

Critical pair: bbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [29].

[29] bbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [28] bbbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbbbbb ba babbbb

Critical pair: bbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [30].

[30] bbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [29] bbbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbbbb ba babbbb

Critical pair: bbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [31].

[31] bbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [30] bbbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbbb ba babbbb

Critical pair: bbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [32].

[32] bbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [31] bbbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bbb ba babbbb

Critical pair: bbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [33].

[33] bba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [32] bbba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

bb ba babbbb

Critical pair: bba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [34].

[34] ba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Overlap of [33] bba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] babbbb=a:

b ba babbbb

Critical pair: ba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Defines rule #2.

Referenced by [35].

[35] abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a

Overlap of [2] babbbb=a with [34] ba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb:

babbbb ba

Critical pair: abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a.

Referenced by [36].

[36] bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1

Overlap of [1] aaa=1 with [35] abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a:

aa a abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Critical pair: aaa=bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce LHS:

[1](aaa)
⇒ 1

Flip LHS and RHS.

Defines rule #1.