Certificate for #13257 ⟨a, b | bab=aba, bba=ba⟩

Back:⟨a, b | bab=aba, bba=ba⟩

Completion settings:

[1] aba=bab

Axiom: bab=aba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[2] bba=ba

Axiom: bba=ba.

Defines rule #1.

Referenced by [3].

[3] babb=bab

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

ab a aba

Critical pair: abbab=babba.

Reduce LHS:

[2]a(bba)b
[1]⇒ (aba)b
⇒ babb

Reduce RHS:

[2]ba(bba)
[1]⇒ b(aba)
[2]⇒ (bba)b
⇒ bab

Defines rule #3.