Certificate for #16175 ⟨a, b | aab=ab, abbb=ba⟩

Back:⟨a, b | aab=ab, abbb=ba⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Defines rule #3.

Referenced by [3].

[2] ba=abbb

Axiom: abbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] abbbbbbbbbb=abbbb

Overlap of [2] ba=abbb with [1] aab=ab:

b a aab

Critical pair: bab=abbbab.

Reduce LHS:

[2](ba)b
⇒ abbbb

Reduce RHS:

[2]abb(ba)b
[2]⇒ ab(ba)bbbb
[2]⇒ a(ba)bbbbbbb
[1]⇒ (aab)bbbbbbbbb
⇒ abbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.