Certificate for #24580 ⟨a, b | ab=a, bbbbbaa=a⟩

Back:⟨a, b | ab=a, bbbbbaa=a⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3].

[2] bbbbbaa=a

Axiom: bbbbbaa=a.

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

[3] aaa=aa

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

a b bbbbbaa

Critical pair: aa=abbbbaa.

Reduce RHS:

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

Flip LHS and RHS.

Referenced by [4].

[4] aa=a

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

bbbbb aa aaa

Critical pair: bbbbbaa=aa.

Reduce LHS:

[2](bbbbbaa)
⇒ a

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

[5] bbbbba=a

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

bbbbb aa aa

Critical pair: bbbbba=a.

Defines rule #3.