Certificate for #21022 ⟨a, b | ab=aa, bbaa=bba⟩

Back:⟨a, b | ab=aa, bbaa=bba⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbaa=bba

Axiom: bbaa=bba.

Defines rule #2.

Referenced by [3].

[3] aaaaa=aaaa

Overlap of [1] ab=aa with [2] bbaa=bba:

a b bbaa

Critical pair: abba=aabaa.

Reduce LHS:

[1](ab)ba
[1]⇒ a(ab)a
⇒ aaaa

Reduce RHS:

[1]a(ab)aa
⇒ aaaaa

Flip LHS and RHS.

Defines rule #3.