Certificate for #19627 ⟨a, b | aab=b, bbbba=bb⟩

Back:⟨a, b | aab=b, bbbba=bb⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3].

[2] bbbba=bb

Axiom: bbbba=bb.

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

[3] bbab=bbbbb

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

bbbb a aab

Critical pair: bbbbb=bbab.

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbbbbbb=bbb

Overlap of [2] bbbba=bb with [3] bbab=bbbbb:

bb bba bbab

Critical pair: bbbbbbb=bbb.

Referenced by [5].

[5] bbbbbb=bb

Overlap of [3] bbab=bbbbb with [2] bbbba=bb:

bba b bbbba

Critical pair: bbabb=bbbbbbbba.

Reduce LHS:

[3](bbab)b
⇒ bbbbbb

Reduce RHS:

[4](bbbbbbb)ba
[2]⇒ (bbbba)
⇒ bb

Defines rule #1.

Referenced by [6].

[6] bba=bbbb

Overlap of [5] bbbbbb=bb with [2] bbbba=bb:

bb bbbb bbbba

Critical pair: bbbb=bba.

Flip LHS and RHS.

Defines rule #2.