Certificate for #25897 ⟨a, b | ab=a, bbbb=aaaa⟩

Back:⟨a, b | ab=a, bbbb=aaaa⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bbbb=aaaa

Axiom: bbbb=aaaa.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaa=a

Overlap of [1] ab=a with [2] bbbb=aaaa:

a b bbbb

Critical pair: aaaaa=abbb.

Reduce RHS:

[1](ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Defines rule #4.

Referenced by [5].

[4] baaaa=aaaa

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

b bbb bbbb

Critical pair: baaaa=aaaab.

Reduce RHS:

[1]aaa(ab)
⇒ aaaa

Referenced by [5].

[5] ba=a

Overlap of [4] baaaa=aaaa with [3] aaaaa=a:

b aaaa aaaaa

Critical pair: ba=aaaaa.

Reduce RHS:

[3](aaaaa)
⇒ a

Defines rule #2.