Certificate for #19085 ⟨a, b | aab=b, bbbbba=b⟩

Back:⟨a, b | aab=b, bbbbba=b⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3].

[2] bbbbba=b

Axiom: bbbbba=b.

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

[3] bab=bbbbbb

Overlap of [2] bbbbba=b with [1] aab=b:

bbbbb a aab

Critical pair: bbbbbb=bab.

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbbbbbbbbb=bb

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

bbbb ba bab

Critical pair: bbbbbbbbbb=bb.

Referenced by [5].

[5] bba=bbbbbb

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

ba b bbbbba

Critical pair: bab=bbbbbbbbbba.

Reduce LHS:

[3](bab)
⇒ bbbbbb

Reduce RHS:

[4](bbbbbbbbbb)a
⇒ bba

Flip LHS and RHS.

Referenced by [6], [7].

[6] bbbbbbbbb=b

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

bbb bba bba

Critical pair: bbbbbbbbb=b.

Defines rule #1.

Referenced by [7].

[7] ba=bbbbb

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

bbbbbbb bb bba

Critical pair: bbbbbbbbbbbbb=ba.

Reduce LHS:

[6](bbbbbbbbb)bbbb
⇒ bbbbb

Flip LHS and RHS.

Defines rule #2.