Certificate for #21044 ⟨a, b | ab=aa, bbbb=baa⟩

Back:⟨a, b | ab=aa, bbbb=baa⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbbb=baa

Axiom: bbbb=baa.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaa=aaaa

Overlap of [1] ab=aa with [2] bbbb=baa:

a b bbbb

Critical pair: abaa=aabbb.

Reduce LHS:

[1](ab)aa
⇒ aaaa

Reduce RHS:

[1]a(ab)bb
[1]⇒ aa(ab)b
[1]⇒ aaa(ab)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.

[4] bbaa=baaa

Overlap of [2] bbbb=baa with [2] bbbb=baa:

b bbb bbbb

Critical pair: bbaa=baab.

Reduce RHS:

[1]ba(ab)
⇒ baaa

Defines rule #2.