Certificate for #5400 ⟨a, b | aab=ba, bab=ba⟩

Back:⟨a, b | aab=ba, bab=ba⟩

Completion settings:

[1] ba=aab

Axiom: aab=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3].

[2] aabb=aab

Axiom: bab=ba.

Reduce LHS:

[1](ba)b
⇒ aabb

Reduce RHS:

[1](ba)
⇒ aab

Defines rule #3.

Referenced by [3].

[3] aaaaaab=aaaab

Overlap of [2] aabb=aab with [1] ba=aab:

aab b ba

Critical pair: aabaab=aaba.

Reduce LHS:

[1]aa(ba)ab
[1]⇒ aaaa(ba)b
[2]⇒ aaaa(aabb)
⇒ aaaaaab

Reduce RHS:

[1]aa(ba)
⇒ aaaab

Defines rule #1.