Certificate for #21040 ⟨a, b | ab=aa, bbbb=aaa⟩

Back:⟨a, b | ab=aa, bbbb=aaa⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbbb=aaa

Axiom: bbbb=aaa.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaa=aaaa

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

a b bbbb

Critical pair: aaaa=aabbb.

Reduce RHS:

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

Flip LHS and RHS.

Defines rule #4.

[4] baaa=aaaa

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

b bbb bbbb

Critical pair: baaa=aaab.

Reduce RHS:

[1]aa(ab)
⇒ aaaa

Defines rule #2.