Certificate for #4190 ⟨a, b | bab=aba, bba=a⟩

Back:⟨a, b | bab=aba, bba=a⟩

Completion settings:

[1] aba=bab

Axiom: bab=aba.

Flip LHS and RHS.

Defines rule #2.

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

[2] bba=a

Axiom: bba=a.

Defines rule #1.

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

[3] aab=baa

Overlap of [1] aba=bab with [1] aba=bab:

ab a aba

Critical pair: abbab=babba.

Reduce LHS:

[2]a(bba)b
⇒ aab

Reduce RHS:

[2]ba(bba)
⇒ baa

Defines rule #3.

Referenced by [4], [5].

[4] aaa=abb

Overlap of [1] aba=bab with [3] aab=baa:

ab a aab

Critical pair: abbaa=babab.

Reduce LHS:

[2]a(bba)a
⇒ aaa

Reduce RHS:

[1]b(aba)b
[2]⇒ (bba)bb
⇒ abb

Defines rule #4.

Referenced by [5].

[5] abbb=ab

Overlap of [4] aaa=abb with [3] aab=baa:

a aa aab

Critical pair: abaa=abbb.

Reduce LHS:

[1](aba)a
[1]⇒ b(aba)
[2]⇒ (bba)b
⇒ ab

Flip LHS and RHS.

Defines rule #5.