Certificate for #16132 ⟨a, b | aab=aa, bbaa=bb⟩

Back:⟨a, b | aab=aa, bbaa=bb⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #1.

Referenced by [3], [4], [5].

[2] bbaa=bb

Axiom: bbaa=bb.

Defines rule #4.

Referenced by [3], [4], [5].

[3] aaaa=aa

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

aa b bbaa

Critical pair: aabb=aabaa.

Reduce LHS:

[1](aab)b
[1]⇒ (aab)
⇒ aa

Reduce RHS:

[1](aab)aa
⇒ aaaa

Flip LHS and RHS.

Defines rule #3.

[4] bbb=bb

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

bb aa aab

Critical pair: bbaa=bbb.

Reduce LHS:

[2](bbaa)
⇒ bb

Flip LHS and RHS.

Defines rule #2.

[5] bbab=bba

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

bba a aab

Critical pair: bbaaa=bbab.

Reduce LHS:

[2](bbaa)a
⇒ bba

Flip LHS and RHS.

Defines rule #5.