Certificate for #2231 ⟨a, b | ab=aa, aaa=bb⟩

Back:⟨a, b | ab=aa, aaa=bb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] aaa=bb

Axiom: aaa=bb.

Defines rule #2.

Referenced by [3], [4].

[3] bbb=bba

Overlap of [2] aaa=bb with [1] ab=aa:

aa a ab

Critical pair: aaaa=bbb.

Reduce LHS:

[2](aaa)a
⇒ bba

Flip LHS and RHS.

Referenced by [5].

[4] bba=bb

Overlap of [2] aaa=bb with [2] aaa=bb:

a aa aaa

Critical pair: abb=bba.

Reduce LHS:

[1](ab)b
[1]⇒ a(ab)
[2]⇒ (aaa)
⇒ bb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bbb=bb

Simplify [3] bbb=bba.

Reduce RHS:

[4](bba)
⇒ bb

Defines rule #4.