Certificate for #6656 ⟨a, b | aab=a, bbba=ba⟩

Back:⟨a, b | aab=a, bbba=ba⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

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

[2] bbba=ba

Axiom: bbba=ba.

Defines rule #3.

Referenced by [3].

[3] abba=aa

Overlap of [1] aab=a with [2] bbba=ba:

aa b bbba

Critical pair: aaba=abba.

Reduce LHS:

[1](aab)a
⇒ aa

Flip LHS and RHS.

Referenced by [4].

[4] aba=aaa

Overlap of [1] aab=a with [3] abba=aa:

a ab abba

Critical pair: aaa=aba.

Flip LHS and RHS.

Referenced by [5], [6].

[5] aaaa=aa

Overlap of [1] aab=a with [4] aba=aaa:

a ab aba

Critical pair: aaaa=aa.

Referenced by [6].

[6] aaa=a

Overlap of [4] aba=aaa with [1] aab=a:

ab a aab

Critical pair: aba=aaaab.

Reduce LHS:

[4](aba)
⇒ aaa

Reduce RHS:

[5](aaaa)b
[1]⇒ (aab)
⇒ a

Defines rule #2.

Referenced by [7].

[7] ab=aa

Overlap of [6] aaa=a with [1] aab=a:

a aa aab

Critical pair: aa=ab.

Flip LHS and RHS.

Defines rule #1.