Certificate for #9382 ⟨a, b | ab=a, bbbb=bba⟩

Back:⟨a, b | ab=a, bbbb=bba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bba=bbbb

Axiom: bbbb=bba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] aa=a

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

a b bba

Critical pair: abbbb=aba.

Reduce LHS:

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

Reduce RHS:

[1](ab)a
⇒ aa

Flip LHS and RHS.

Defines rule #4.

[4] bbbbb=bbbb

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

bb a ab

Critical pair: bba=bbbbb.

Reduce LHS:

[2](bba)
⇒ bbbb

Flip LHS and RHS.

Defines rule #1.