Certificate for #1685 ⟨a, b | aba=bb, bbb=b⟩

Back:⟨a, b | aba=bb, bbb=b⟩

Completion settings:

[1] aba=bb

Axiom: aba=bb.

Referenced by [3], [4].

[2] bbb=b

Axiom: bbb=b.

Defines rule #3.

Referenced by [3].

[3] ba=ab

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

ab a aba

Critical pair: abbb=bbba.

Reduce LHS:

[2]a(bbb)
⇒ ab

Reduce RHS:

[2](bbb)a
⇒ ba

Flip LHS and RHS.

Defines rule #1.

Referenced by [4].

[4] aab=bb

Overlap of [1] aba=bb with [3] ba=ab:

a ba ba

Critical pair: aab=bb.

Defines rule #2.