Certificate for #25102 ⟨a, b | ab=a, bbbbaa=ba⟩

Back:⟨a, b | ab=a, bbbbaa=ba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] bbbbaa=ba

Axiom: bbbbaa=ba.

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

[3] aaa=aa

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

a b bbbbaa

Critical pair: aba=abbbaa.

Reduce LHS:

[1](ab)a
⇒ aa

Reduce RHS:

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

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] baa=ba

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

bbbb aa aaa

Critical pair: bbbbaa=baa.

Reduce LHS:

[2](bbbbaa)
⇒ ba

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bbbba=ba

Overlap of [2] bbbbaa=ba with [4] baa=ba:

bbb baa baa

Critical pair: bbbba=ba.

Defines rule #4.