Certificate for #25658 ⟨a, b | ab=a, bbbbb=bba⟩

Back:⟨a, b | ab=a, bbbbb=bba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bbbbb=bba

Axiom: bbbbb=bba.

Defines rule #4.

Referenced by [3], [4].

[3] aa=a

Overlap of [1] ab=a with [2] bbbbb=bba:

a b bbbbb

Critical pair: abba=abbbb.

Reduce LHS:

[1](ab)ba
[1]⇒ (ab)a
⇒ aa

Reduce RHS:

[1](ab)bbb
[1]⇒ (ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Defines rule #1.

[4] bbba=bba

Overlap of [2] bbbbb=bba with [2] bbbbb=bba:

b bbbb bbbbb

Critical pair: bbba=bbab.

Reduce RHS:

[1]bb(ab)
⇒ bba

Defines rule #3.