Certificate for #16041 ⟨a, b | aaa=ab, bbbb=aa⟩

Back:⟨a, b | aaa=ab, bbbb=aa⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[2] bbbb=aa

Axiom: bbbb=aa.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaaaaaa=aaa

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

a b bbbb

Critical pair: aaa=aaabbb.

Reduce RHS:

[1]aa(ab)bb
[1]⇒ aaaa(ab)b
[1]⇒ aaaaaa(ab)
⇒ aaaaaaaaa

Flip LHS and RHS.

Defines rule #1.

[4] baa=aaaa

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

b bbb bbbb

Critical pair: baa=aab.

Reduce RHS:

[1]a(ab)
⇒ aaaa

Defines rule #2.