Certificate for #8832 ⟨a, b | ab=a, bbbbaa=a⟩

Back:⟨a, b | ab=a, bbbbaa=a⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3].

[2] bbbbaa=a

Axiom: bbbbaa=a.

Referenced by [3], [4], [5].

[3] aaa=aa

Overlap of [1] ab=a with [2] bbbbaa=a:

a b bbbbaa

Critical pair: aa=abbbaa.

Reduce RHS:

[1](ab)bbaa
[1]⇒ (ab)baa
[1]⇒ (ab)aa
⇒ aaa

Flip LHS and RHS.

Referenced by [4].

[4] aa=a

Overlap of [2] bbbbaa=a with [3] aaa=aa:

bbbb aa aaa

Critical pair: bbbbaa=aa.

Reduce LHS:

[2](bbbbaa)
⇒ a

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

[5] bbbba=a

Overlap of [2] bbbbaa=a with [4] aa=a:

bbbb aa aa

Critical pair: bbbba=a.

Defines rule #3.