Certificate for #15670 ⟨a, b | aab=ab, bbbba=b⟩

Back:⟨a, b | aab=ab, bbbba=b⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Defines rule #2.

Referenced by [3].

[2] bbbba=b

Axiom: bbbba=b.

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

[3] bab=bb

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

bbbb a aab

Critical pair: bbbbab=bab.

Reduce LHS:

[2](bbbba)b
⇒ bb

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbbbb=bb

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

bbb ba bab

Critical pair: bbbbb=bb.

Referenced by [5].

[5] bba=bb

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

ba b bbbba

Critical pair: bab=bbbbba.

Reduce LHS:

[3](bab)
⇒ bb

Reduce RHS:

[4](bbbbb)a
⇒ bba

Flip LHS and RHS.

Referenced by [6], [7].

[6] bbbb=b

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

bb bba bba

Critical pair: bbbb=b.

Defines rule #3.

Referenced by [7].

[7] ba=b

Overlap of [6] bbbb=b with [5] bba=bb:

bb bb bba

Critical pair: bbbb=ba.

Reduce LHS:

[6](bbbb)
⇒ b

Flip LHS and RHS.

Defines rule #1.