Certificate for #3024 ⟨a, b | aa=a, abbb=ba⟩

Back:⟨a, b | aa=a, abbb=ba⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #3.

Referenced by [3].

[2] ba=abbb

Axiom: abbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] abbbbbbbbb=abbb

Overlap of [2] ba=abbb with [1] aa=a:

b a aa

Critical pair: ba=abbba.

Reduce LHS:

[2](ba)
⇒ abbb

Reduce RHS:

[2]abb(ba)
[2]⇒ ab(ba)bbb
[2]⇒ a(ba)bbbbbb
[1]⇒ (aa)bbbbbbbbb
⇒ abbbbbbbbb

Flip LHS and RHS.

Defines rule #1.