Certificate for #25246 ⟨a, b | aa=a, babbb=bba

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #3.

Referenced by [3].

[2] bba=babbb

Axiom: babbb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] bababbbbbb=babbb

Overlap of [2] bba=babbb with [1] aa=a:

bb a aa

Critical pair: bba=babbba.

Reduce LHS:

[2](bba)
babbb

Reduce RHS:

[2]bab(bba)
[2]ba(bba)bbb
bababbbbbb

Flip LHS and RHS.

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

[4] babbbbbbbbbbbb=babbbbbb

Overlap of [2] bba=babbb with [3] bababbbbbb=babbb:

b ba bababbbbbb

Critical pair: bbabbb=babbbbabbbbbb.

Reduce LHS:

[2](bba)bbb
babbbbbb

Reduce RHS:

[2]babb(bba)bbbbbb
[2]bab(bba)bbbbbbbbb
[2]ba(bba)bbbbbbbbbbbb
[3](bababbbbbb)bbbbbbbbb
babbbbbbbbbbbb

Flip LHS and RHS.

Referenced by [5].

[5] babbbbbbbbb=babbb

Overlap of [3] bababbbbbb=babbb with [4] babbbbbbbbbbbb=babbbbbb:

ba babbbbbb babbbbbbbbbbbb

Critical pair: bababbbbbb=babbbbbbbbb.

Reduce LHS:

[3](bababbbbbb)
babbb

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

[6] bababbb=babbbbbb

Overlap of [3] bababbbbbb=babbb with [5] babbbbbbbbb=babbb:

ba babbbbbb babbbbbbbbb

Critical pair: bababbb=babbbbbb.

Defines rule #4.