Certificate for #5372 ⟨a, b | aab=aa, bba=bb⟩

Back:⟨a, b | aab=aa, bba=bb⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #2.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #3.

Referenced by [3], [4].

[3] aaa=aa

Overlap of [1] aab=aa with [2] bba=bb:

aa b bba

Critical pair: aabb=aaba.

Reduce LHS:

[1](aab)b
[1]⇒ (aab)
⇒ aa

Reduce RHS:

[1](aab)a
⇒ aaa

Flip LHS and RHS.

Defines rule #1.

[4] bbb=bb

Overlap of [2] bba=bb with [1] aab=aa:

bb a aab

Critical pair: bbaa=bbab.

Reduce LHS:

[2](bba)a
[2]⇒ (bba)
⇒ bb

Reduce RHS:

[2](bba)b
⇒ bbb

Flip LHS and RHS.

Defines rule #4.