Certificate for #20632 ⟨a, b | ab=aa, bbbaaa=a⟩

Back:⟨a, b | ab=aa, bbbaaa=a⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbbaaa=a

Axiom: bbbaaa=a.

Referenced by [3], [4], [5], [6].

[3] aaaaaaa=aa

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

a b bbbaaa

Critical pair: aa=aabbaaa.

Reduce RHS:

[1]a(ab)baaa
[1]⇒ aa(ab)aaa
⇒ aaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbbaa=aaaaa

Overlap of [2] bbbaaa=a with [3] aaaaaaa=aa:

bbb aaa aaaaaaa

Critical pair: bbbaa=aaaaa.

Referenced by [5].

[5] aaaaaa=a

Overlap of [2] bbbaaa=a with [4] bbbaa=aaaaa:

bbbaaa bbbaa

Critical pair: aaaaaa=a.

Defines rule #3.

Referenced by [6].

[6] bbba=aaaa

Overlap of [2] bbbaaa=a with [5] aaaaaa=a:

bbb aaa aaaaaa

Critical pair: bbba=aaaa.

Defines rule #2.