Certificate for #9083 ⟨a, b | ab=a, bbaaa=bb⟩

Back:⟨a, b | ab=a, bbaaa=bb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bbaaa=bb

Axiom: bbaaa=bb.

Defines rule #4.

Referenced by [3], [4].

[3] aaaa=a

Overlap of [1] ab=a with [2] bbaaa=bb:

a b bbaaa

Critical pair: abb=abaaa.

Reduce LHS:

[1](ab)b
[1]⇒ (ab)
⇒ a

Reduce RHS:

[1](ab)aaa
⇒ aaaa

Flip LHS and RHS.

Defines rule #3.

[4] bbb=bb

Overlap of [2] bbaaa=bb with [1] ab=a:

bbaa a ab

Critical pair: bbaaa=bbb.

Reduce LHS:

[2](bbaaa)
⇒ bb

Flip LHS and RHS.

Defines rule #2.