Certificate for #15798 ⟨a, b | aab=bb, bbbba=b⟩

Back:⟨a, b | aab=bb, bbbba=b⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #3.

Referenced by [3].

[2] bbbba=b

Axiom: bbbba=b.

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

[3] bab=bbbbbb

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

bbbb a aab

Critical pair: bbbbbb=bab.

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbbbbbbbb=bb

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

bbb ba bab

Critical pair: bbbbbbbbb=bb.

Referenced by [5].

[5] bba=bbbbbb

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

ba b bbbba

Critical pair: bab=bbbbbbbbba.

Reduce LHS:

[3](bab)
⇒ bbbbbb

Reduce RHS:

[4](bbbbbbbbb)a
⇒ bba

Flip LHS and RHS.

Referenced by [6], [7].

[6] bbbbbbbb=b

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

bb bba bba

Critical pair: bbbbbbbb=b.

Defines rule #1.

Referenced by [7].

[7] ba=bbbbb

Overlap of [6] bbbbbbbb=b with [5] bba=bbbbbb:

bbbbbb bb bba

Critical pair: bbbbbbbbbbbb=ba.

Reduce LHS:

[6](bbbbbbbb)bbbb
⇒ bbbbb

Flip LHS and RHS.

Defines rule #2.