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] bba=bbbbb

Axiom: bbbbb=bba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] aa=a

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

a b bba

Critical pair: abbbbb=aba.

Reduce LHS:

[1](ab)bbbb
[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] bbbbbb=bbbbb

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

bb a ab

Critical pair: bba=bbbbbb.

Reduce LHS:

[2](bba)
⇒ bbbbb

Flip LHS and RHS.

Defines rule #1.