Certificate for #13130 ⟨a, b | aab=aaa, baa=ba⟩

Back:⟨a, b | aab=aaa, baa=ba⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #1.

Referenced by [3], [4].

[2] baa=ba

Axiom: baa=ba.

Defines rule #2.

Referenced by [3], [4].

[3] aaaaa=aaaa

Overlap of [1] aab=aaa with [2] baa=ba:

aa b baa

Critical pair: aaba=aaaaa.

Reduce LHS:

[1](aab)a
⇒ aaaa

Flip LHS and RHS.

Defines rule #4.

[4] bab=ba

Overlap of [2] baa=ba with [1] aab=aaa:

b aa aab

Critical pair: baaa=bab.

Reduce LHS:

[2](baa)a
[2]⇒ (baa)
⇒ ba

Flip LHS and RHS.

Defines rule #3.