Certificate for #6998 ⟨a, b | ab=aa, bbaaa=a⟩

Back:⟨a, b | ab=aa, bbaaa=a⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbaaa=a

Axiom: bbaaa=a.

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

[3] aaaaaa=aa

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

a b bbaaa

Critical pair: aa=aabaaa.

Reduce RHS:

[1]a(ab)aaa
⇒ aaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbaa=aaaa

Overlap of [2] bbaaa=a with [3] aaaaaa=aa:

bb aaa aaaaaa

Critical pair: bbaa=aaaa.

Referenced by [5].

[5] aaaaa=a

Overlap of [2] bbaaa=a with [4] bbaa=aaaa:

bbaaa bbaa

Critical pair: aaaaa=a.

Defines rule #3.

Referenced by [6].

[6] bba=aaa

Overlap of [2] bbaaa=a with [5] aaaaa=a:

bb aaa aaaaa

Critical pair: bba=aaa.

Defines rule #2.