Certificate for #27121 ⟨a, b | aa=1, ababbab=bb

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #4.

Referenced by [3], [6], [13], [14].

[2] ababbab=bb

Axiom: ababbab=bb.

Referenced by [3], [4], [7].

[3] babbab=abb

Overlap of [1] aa=1 with [2] ababbab=bb:

a a ababbab

Critical pair: abb=babbab.

Flip LHS and RHS.

Referenced by [4], [5], [8], [9], [11].

[4] ababb=babbbb

Overlap of [3] babbab=abb with [2] ababbab=bb:

babb ab ababbab

Critical pair: babbbb=abbabbab.

Reduce RHS:

[3]ab(babbab)
ababb

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6], [7], [8], [11], [12], [14].

[5] abbbab=bbabbbb

Overlap of [3] babbab=abb with [3] babbab=abb:

bab bab babbab

Critical pair: bababb=abbbab.

Reduce LHS:

[4]b(ababb)
bbabbbb

Flip LHS and RHS.

Defines rule #7.

Referenced by [8], [9].

[6] babbbbbb=babb

Overlap of [1] aa=1 with [4] ababb=babbbb:

a a ababb

Critical pair: ababbbb=babb.

Reduce LHS:

[4](ababb)bb
babbbbbb

Referenced by [8], [11].

[7] babbbbab=bb

Overlap of [2] ababbab=bb with [4] ababb=babbbb:

ababbab ababb

Critical pair: babbbbab=bb.

Referenced by [9], [10], [12], [13], [14].

[8] abbabb=bbbabbb

Overlap of [3] babbab=abb with [4] ababb=babbbb:

babb ab ababb

Critical pair: babbbabbbb=abbabb.

Reduce LHS:

[5]b(abbbab)bbb
[6]bb(babbbbbb)b
bbbabbb

Flip LHS and RHS.

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

[9] bbbabbbbb=bbbab

Overlap of [7] babbbbab=bb with [3] babbab=abb:

babbb bab babbab

Critical pair: babbbabb=bbbab.

Reduce LHS:

[5]b(abbbab)b
bbbabbbbb

Referenced by [10], [11].

[10] bbbabab=abbb

Overlap of [8] abbabb=bbbabbb with [7] babbbbab=bb:

ab babb babbbbab

Critical pair: abbb=bbbabbbbbab.

Reduce RHS:

[9](bbbabbbbb)ab
bbbabab

Flip LHS and RHS.

Referenced by [11], [12], [13], [15].

[11] abbab=bbbabb

Overlap of [4] ababb=babbbb with [10] bbbabab=abbb:

abab b bbbabab

Critical pair: abababbb=babbbbbbabab.

Reduce LHS:

[4]ab(ababb)b
[8](abbabb)bbb
[9](bbbabbbbb)b
bbbabb

Reduce RHS:

[6](babbbbbb)abab
[3](babbab)ab
abbab

Flip LHS and RHS.

Defines rule #6.

Referenced by [14].

[12] bbabbbbb=bbab

Overlap of [7] babbbbab=bb with [10] bbbabab=abbb:

bab bbbab bbbabab

Critical pair: bababbb=bbab.

Reduce LHS:

[4]b(ababb)b
bbabbbbb

Defines rule #2.

[13] bbbbab=abbbbb

Overlap of [8] abbabb=bbbabbb with [10] bbbabab=abbb:

abba bb bbbabab

Critical pair: abbaabbb=bbbabbbbabab.

Reduce LHS:

[1]abb(aa)bbb
abbbbb

Reduce RHS:

[7]bb(babbbbab)ab
bbbbab

Flip LHS and RHS.

Defines rule #3.

Referenced by [14].

[14] bbbbbb=bb

Overlap of [4] ababb=babbbb with [11] abbab=bbbabb:

ab abb abbab

Critical pair: abbbbabb=babbbbab.

Reduce LHS:

[13]a(bbbbab)b
[1](aa)bbbbbb
bbbbbb

Reduce RHS:

[7](babbbbab)
bb

Defines rule #1.

Referenced by [15].

[15] bbabab=bbbabbb

Overlap of [14] bbbbbb=bb with [10] bbbabab=abbb:

bbb bbb bbbabab

Critical pair: bbbabbb=bbabab.

Flip LHS and RHS.

Defines rule #8.