Certificate for #13134 ⟨a, b | aab=aaa, bab=ba⟩

Back:⟨a, b | aab=aaa, bab=ba⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #1.

Referenced by [3], [4].

[2] bab=ba

Axiom: bab=ba.

Defines rule #2.

Referenced by [3], [4].

[3] baaa=baa

Overlap of [2] bab=ba with [2] bab=ba:

ba b bab

Critical pair: baba=baab.

Reduce LHS:

[2](bab)a
⇒ baa

Reduce RHS:

[1]b(aab)
⇒ baaa

Flip LHS and RHS.

Defines rule #3.

[4] aaaaa=aaaa

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

aa b bab

Critical pair: aaba=aaaab.

Reduce LHS:

[1](aab)a
⇒ aaaa

Reduce RHS:

[1]aa(aab)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.