Certificate for #21039 ⟨a, b | ab=aa, bbba=bbb⟩

Back:⟨a, b | ab=aa, bbba=bbb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbba=bbb

Axiom: bbba=bbb.

Defines rule #2.

Referenced by [3], [4].

[3] aaaaa=aaaa

Overlap of [1] ab=aa with [2] bbba=bbb:

a b bbba

Critical pair: abbb=aabba.

Reduce LHS:

[1](ab)bb
[1]⇒ a(ab)b
[1]⇒ aa(ab)
⇒ aaaa

Reduce RHS:

[1]a(ab)ba
[1]⇒ aa(ab)a
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.

[4] bbbb=bbb

Overlap of [2] bbba=bbb with [1] ab=aa:

bbb a ab

Critical pair: bbbaa=bbbb.

Reduce LHS:

[2](bbba)a
[2]⇒ (bbba)
⇒ bbb

Flip LHS and RHS.

Defines rule #3.