Certificate for #25635 ⟨a, b | ab=a, bbbaa=bbb⟩

Back:⟨a, b | ab=a, bbbaa=bbb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bbbaa=bbb

Axiom: bbbaa=bbb.

Defines rule #4.

Referenced by [3], [4].

[3] aaa=a

Overlap of [1] ab=a with [2] bbbaa=bbb:

a b bbbaa

Critical pair: abbb=abbaa.

Reduce LHS:

[1](ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Reduce RHS:

[1](ab)baa
[1]⇒ (ab)aa
⇒ aaa

Flip LHS and RHS.

Defines rule #2.

[4] bbbb=bbb

Overlap of [2] bbbaa=bbb with [1] ab=a:

bbba a ab

Critical pair: bbbaa=bbbb.

Reduce LHS:

[2](bbbaa)
⇒ bbb

Flip LHS and RHS.

Defines rule #3.