Certificate for #2890 ⟨a, b | aa=a, babbb=a

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #3.

Referenced by [3], [4], [5], [6].

[2] babbb=a

Axiom: babbb=a.

Referenced by [3], [4], [6], [7], [10].

[3] babba=abbb

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

babb b babbb

Critical pair: babba=aabbb.

Reduce RHS:

[1](aa)bbb
abbb

Referenced by [4], [5], [6], [7].

[4] abba=abbbbbb

Overlap of [2] babbb=a with [3] babba=abbb:

babb b babba

Critical pair: babbabbb=aabba.

Reduce LHS:

[3](babba)bbb
abbbbbb

Reduce RHS:

[1](aa)bba
abba

Flip LHS and RHS.

Referenced by [8].

[5] abbba=abbb

Overlap of [3] babba=abbb with [1] aa=a:

babb a aa

Critical pair: babba=abbba.

Reduce LHS:

[3](babba)
abbb

Flip LHS and RHS.

Referenced by [7], [9].

[6] abbbbba=ba

Overlap of [3] babba=abbb with [3] babba=abbb:

bab ba babba

Critical pair: bababbb=abbbbba.

Reduce LHS:

[2]ba(babbb)
[1]b(aa)
ba

Flip LHS and RHS.

Referenced by [7], [9].

[7] aba=ba

Overlap of [5] abbba=abbb with [3] babba=abbb:

abb ba babba

Critical pair: abbabbb=abbbbba.

Reduce LHS:

[2]ab(babbb)
aba

Reduce RHS:

[6](abbbbba)
ba

Referenced by [8].

[8] bba=abbbbbb

Overlap of [7] aba=ba with [7] aba=ba:

ab a aba

Critical pair: abba=baba.

Reduce LHS:

[4](abba)
abbbbbb

Reduce RHS:

[7]b(aba)
bba

Flip LHS and RHS.

Referenced by [9].

[9] ba=abbbbbbbbb

Simplify [6] abbbbba=ba.

Reduce LHS:

[8]abbb(bba)
[5](abbba)bbbbbb
abbbbbbbbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

[10] abbbbbbbbbbbb=a

Overlap of [2] babbb=a with [9] ba=abbbbbbbbb:

babbb ba

Critical pair: abbbbbbbbbbbb=a.

Defines rule #1.