Certificate for #16458 ⟨a, b | aba=bb, abba=bb⟩

Back:⟨a, b | aba=bb, abba=bb⟩

Completion settings:

[1] aba=bb

Axiom: aba=bb.

Defines rule #1.

Referenced by [3], [4], [5], [6], [7].

[2] abba=bb

Axiom: abba=bb.

Defines rule #3.

Referenced by [4], [5].

[3] abbb=bbba

Overlap of [1] aba=bb with [1] aba=bb:

ab a aba

Critical pair: abbb=bbba.

Defines rule #2.

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

[4] bbbba=bbba

Overlap of [1] aba=bb with [2] abba=bb:

ab a abba

Critical pair: abbb=bbbba.

Reduce LHS:

[3](abbb)
⇒ bbba

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

[5] bbbab=bbba

Overlap of [2] abba=bb with [1] aba=bb:

abb a aba

Critical pair: abbbb=bbba.

Reduce LHS:

[3](abbb)b
⇒ bbbab

Defines rule #5.

Referenced by [6], [7].

[6] bbbaa=bbbbb

Overlap of [1] aba=bb with [3] abbb=bbba:

ab a abbb

Critical pair: abbbba=bbbbb.

Reduce LHS:

[3](abbb)ba
[5]⇒ (bbbab)a
⇒ bbbaa

Defines rule #6.

Referenced by [7].

[7] bbbbbb=bbbbb

Overlap of [4] bbbba=bbba with [1] aba=bb:

bbbb a aba

Critical pair: bbbbbb=bbbaba.

Reduce RHS:

[5](bbbab)a
[6]⇒ (bbbaa)
⇒ bbbbb

Defines rule #7.