Certificate for #5406 ⟨a, b | aab=bb, aba=ba⟩

Back:⟨a, b | aab=bb, aba=ba⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #1.

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

[2] aba=ba

Axiom: aba=ba.

Defines rule #2.

Referenced by [3], [4].

[3] bba=ba

Overlap of [1] aab=bb with [2] aba=ba:

a ab aba

Critical pair: aba=bba.

Reduce LHS:

[2](aba)
⇒ ba

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[4] abbb=bbb

Overlap of [2] aba=ba with [1] aab=bb:

ab a aab

Critical pair: abbb=baab.

Reduce RHS:

[1]b(aab)
⇒ bbb

Defines rule #4.

[5] bbbb=bbb

Overlap of [3] bba=ba with [1] aab=bb:

bb a aab

Critical pair: bbbb=baab.

Reduce RHS:

[1]b(aab)
⇒ bbb

Defines rule #5.