Certificate for #2584 ⟨a, b | aaa=1, abbb=ba⟩

Back:⟨a, b | aaa=1, abbb=ba⟩

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #3.

Referenced by [3].

[2] ba=abbb

Axiom: abbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] bbbbbbbbbbbbbbbbbbbbbbbbbbb=b

Overlap of [2] ba=abbb with [1] aaa=1:

b a aaa

Critical pair: b=abbbaa.

Reduce RHS:

[2]abb(ba)a
[2]⇒ ab(ba)bbba
[2]⇒ a(ba)bbbbbba
[2]⇒ aabbbbbbbb(ba)
[2]⇒ aabbbbbbb(ba)bbb
[2]⇒ aabbbbbb(ba)bbbbbb
[2]⇒ aabbbbb(ba)bbbbbbbbb
[2]⇒ aabbbb(ba)bbbbbbbbbbbb
[2]⇒ aabbb(ba)bbbbbbbbbbbbbbb
[2]⇒ aabb(ba)bbbbbbbbbbbbbbbbbb
[2]⇒ aab(ba)bbbbbbbbbbbbbbbbbbbbb
[2]⇒ aa(ba)bbbbbbbbbbbbbbbbbbbbbbbb
[1]⇒ (aaa)bbbbbbbbbbbbbbbbbbbbbbbbbbb
⇒ bbbbbbbbbbbbbbbbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.