Certificate for #24572 ⟨a, b | ab=a, bbbbaaa=a⟩

Back:⟨a, b | ab=a, bbbbaaa=a⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] bbbbaaa=a

Axiom: bbbbaaa=a.

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

[3] aaaa=aa

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

a b bbbbaaa

Critical pair: aa=abbbaaa.

Reduce RHS:

[1](ab)bbaaa
[1]⇒ (ab)baaa
[1]⇒ (ab)aaa
⇒ aaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbbbaa=aa

Overlap of [2] bbbbaaa=a with [3] aaaa=aa:

bbbb aaa aaaa

Critical pair: bbbbaa=aa.

Referenced by [5], [6].

[5] aaa=a

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

bbbbaaa bbbbaa

Critical pair: aaa=a.

Defines rule #2.

Referenced by [6].

[6] bbbba=a

Overlap of [4] bbbbaa=aa with [5] aaa=a:

bbbb aa aaa

Critical pair: bbbba=aaa.

Reduce RHS:

[5](aaa)
⇒ a

Defines rule #3.