Certificate for #16135 ⟨a, b | aab=aa, bbab=ba⟩

Back:⟨a, b | aab=aa, bbab=ba⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #1.

Referenced by [4], [5].

[2] bbab=ba

Axiom: bbab=ba.

Defines rule #3.

Referenced by [3], [4].

[3] babab=baa

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

bba b bbab

Critical pair: bbaba=babab.

Reduce LHS:

[2](bbab)a
⇒ baa

Flip LHS and RHS.

Defines rule #5.

Referenced by [4], [5].

[4] bbaa=baa

Overlap of [2] bbab=ba with [3] babab=baa:

b bab babab

Critical pair: bbaa=baab.

Reduce RHS:

[1]b(aab)
⇒ baa

Defines rule #2.

[5] babaa=baaa

Overlap of [3] babab=baa with [3] babab=baa:

ba bab babab

Critical pair: babaa=baaab.

Reduce RHS:

[1]ba(aab)
⇒ baaa

Defines rule #4.