Certificate for #13139 ⟨a, b | aab=aaa, bba=bb⟩

Back:⟨a, b | aab=aaa, bba=bb⟩

Completion settings:

[1] aaa=aab

Axiom: aab=aaa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #2.

Referenced by [4].

[3] aaba=aabb

Overlap of [1] aaa=aab with [1] aaa=aab:

a aa aaa

Critical pair: aaab=aaba.

Reduce LHS:

[1](aaa)b
⇒ aabb

Flip LHS and RHS.

Defines rule #4.

[4] bbb=bb

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

bb a aaa

Critical pair: bbaab=bbaa.

Reduce LHS:

[2](bba)ab
[2]⇒ (bba)b
⇒ bbb

Reduce RHS:

[2](bba)a
[2]⇒ (bba)
⇒ bb

Defines rule #1.