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

Back:⟨a, b | aab=aaa, bba=bb⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #1.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #2.

Referenced by [3], [4].

[3] aaaaa=aaaa

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

aa b bba

Critical pair: aabb=aaaba.

Reduce LHS:

[1](aab)b
[1]⇒ a(aab)
⇒ aaaa

Reduce RHS:

[1]a(aab)a
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.

[4] bbb=bb

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

bb a aab

Critical pair: bbaaa=bbab.

Reduce LHS:

[2](bba)aa
[2]⇒ (bba)a
[2]⇒ (bba)
⇒ bb

Reduce RHS:

[2](bba)b
⇒ bbb

Flip LHS and RHS.

Defines rule #3.