Certificate for #1631 ⟨a, b | aab=ab, bba=b⟩

Back:⟨a, b | aab=ab, bba=b⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Defines rule #3.

Referenced by [3].

[2] bba=b

Axiom: bba=b.

Referenced by [3], [4], [5], [6].

[3] bab=bb

Overlap of [2] bba=b with [1] aab=ab:

bb a aab

Critical pair: bbab=bab.

Reduce LHS:

[2](bba)b
⇒ bb

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbb=bb

Overlap of [2] bba=b with [3] bab=bb:

b ba bab

Critical pair: bbb=bb.

Referenced by [5].

[5] bb=b

Overlap of [3] bab=bb with [2] bba=b:

ba b bba

Critical pair: bab=bbba.

Reduce LHS:

[3](bab)
⇒ bb

Reduce RHS:

[4](bbb)a
[2]⇒ (bba)
⇒ b

Defines rule #2.

Referenced by [6].

[6] ba=b

Overlap of [2] bba=b with [5] bb=b:

bba bb

Critical pair: ba=b.

Defines rule #1.