Certificate for #9747 ⟨a, b | aa=1, abbabba=b

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #4.

Referenced by [3], [4], [6], [10].

[2] abbabba=b

Axiom: abbabba=b.

Referenced by [3], [4], [5].

[3] bbabba=ab

Overlap of [1] aa=1 with [2] abbabba=b:

a a abbabba

Critical pair: ab=bbabba.

Flip LHS and RHS.

Referenced by [9].

[4] abbabb=ba

Overlap of [2] abbabba=b with [1] aa=1:

abbabb a aa

Critical pair: abbabb=ba.

Referenced by [6], [7], [8].

[5] bbba=abbb

Overlap of [2] abbabba=b with [2] abbabba=b:

abb abba abbabba

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [8], [9], [11].

[6] aba=bbabb

Overlap of [1] aa=1 with [4] abbabb=ba:

a a abbabb

Critical pair: aba=bbabb.

Defines rule #5.

Referenced by [7], [8].

[7] babba=bbabbbbbbbbbb

Overlap of [4] abbabb=ba with [5] bbba=abbb:

abbab b bbba

Critical pair: abbababbb=babba.

Reduce LHS:

[6]abb(aba)bbb
[5]ab(bbba)bbbbb
[6](aba)bbbbbbbb
bbabbbbbbbbbb

Flip LHS and RHS.

Referenced by [9].

[8] abba=babbbbbbbbbb

Overlap of [6] aba=bbabb with [4] abbabb=ba:

ab a abbabb

Critical pair: abba=bbabbbbabb.

Reduce RHS:

[5]bbab(bbba)bb
[6]bb(aba)bbbbb
[5]b(bbba)bbbbbbb
babbbbbbbbbb

Defines rule #6.

[9] abbbbbbbbbbbbb=ab

Simplify [3] bbabba=ab.

Reduce LHS:

[7]b(babba)
[5](bbba)bbbbbbbbbb
abbbbbbbbbbbbb

Referenced by [10].

[10] bbbbbbbbbbbbb=b

Overlap of [1] aa=1 with [9] abbbbbbbbbbbbb=ab:

a a abbbbbbbbbbbbb

Critical pair: aab=bbbbbbbbbbbbb.

Reduce LHS:

[1](aa)b
b

Flip LHS and RHS.

Defines rule #1.

Referenced by [11].

[11] babbbbbbbbbbbb=ba

Overlap of [10] bbbbbbbbbbbbb=b with [5] bbba=abbb:

bbbbbbbbbb bbb bbba

Critical pair: bbbbbbbbbbabbb=ba.

Reduce LHS:

[5]bbbbbbb(bbba)bbb
[5]bbbb(bbba)bbbbbb
[5]b(bbba)bbbbbbbbb
babbbbbbbbbbbb

Defines rule #2.