Certificate for #2984 ⟨a, b | ab=a, bbaaa=a⟩

Back:⟨a, b | ab=a, bbaaa=a⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] bbaaa=a

Axiom: bbaaa=a.

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

[3] aaaa=aa

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

a b bbaaa

Critical pair: aa=abaaa.

Reduce RHS:

[1](ab)aaa
⇒ aaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbaa=aa

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

bb aaa aaaa

Critical pair: bbaa=aa.

Referenced by [5], [6].

[5] aaa=a

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

bbaaa bbaa

Critical pair: aaa=a.

Defines rule #2.

Referenced by [6].

[6] bba=a

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

bb aa aaa

Critical pair: bba=aaa.

Reduce RHS:

[5](aaa)
⇒ a

Defines rule #3.