Certificate for #25086 ⟨a, b | ab=a, bbbaaa=ba⟩

Back:⟨a, b | ab=a, bbbaaa=ba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] bbbaaa=ba

Axiom: bbbaaa=ba.

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

[3] aaaa=aa

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

a b bbbaaa

Critical pair: aba=abbaaa.

Reduce LHS:

[1](ab)a
⇒ aa

Reduce RHS:

[1](ab)baaa
[1]⇒ (ab)aaa
⇒ aaaa

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] bbbaa=baa

Overlap of [2] bbbaaa=ba with [3] aaaa=aa:

bbb aaa aaaa

Critical pair: bbbaa=baa.

Referenced by [5], [6].

[5] baaa=ba

Overlap of [2] bbbaaa=ba with [4] bbbaa=baa:

bbbaaa bbbaa

Critical pair: baaa=ba.

Defines rule #3.

Referenced by [6].

[6] bbba=ba

Overlap of [4] bbbaa=baa with [5] baaa=ba:

bb baa baaa

Critical pair: bbba=baaa.

Reduce RHS:

[5](baaa)
⇒ ba

Defines rule #4.