Certificate for #16143 ⟨a, b | aab=aa, bbbb=ba⟩

Back:⟨a, b | aab=aa, bbbb=ba⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #3.

Referenced by [3], [4].

[2] ba=bbbb

Axiom: bbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaa=aa

Overlap of [1] aab=aa with [2] ba=bbbb:

aa b ba

Critical pair: aabbbb=aaa.

Reduce LHS:

[1](aab)bbb
[1]⇒ (aab)bb
[1]⇒ (aab)b
[1]⇒ (aab)
⇒ aa

Flip LHS and RHS.

Defines rule #4.

[4] bbbbbbbb=bbbbbbb

Overlap of [2] ba=bbbb with [1] aab=aa:

b a aab

Critical pair: baa=bbbbab.

Reduce LHS:

[2](ba)a
[2]⇒ bbb(ba)
⇒ bbbbbbb

Reduce RHS:

[2]bbb(ba)b
⇒ bbbbbbbb

Flip LHS and RHS.

Defines rule #1.