Certificate for #2081 ⟨a, b | aab=b, bbba=b⟩

Back:⟨a, b | aab=b, bbba=b⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3].

[2] bbba=b

Axiom: bbba=b.

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

[3] bab=bbbb

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

bbb a aab

Critical pair: bbbb=bab.

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbbbbb=bb

Overlap of [2] bbba=b with [3] bab=bbbb:

bb ba bab

Critical pair: bbbbbb=bb.

Referenced by [5].

[5] bba=bbbb

Overlap of [3] bab=bbbb with [2] bbba=b:

ba b bbba

Critical pair: bab=bbbbbba.

Reduce LHS:

[3](bab)
⇒ bbbb

Reduce RHS:

[4](bbbbbb)a
⇒ bba

Flip LHS and RHS.

Referenced by [6], [7].

[6] bbbbb=b

Overlap of [2] bbba=b with [5] bba=bbbb:

b bba bba

Critical pair: bbbbb=b.

Defines rule #1.

Referenced by [7].

[7] ba=bbb

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

bbb bb bba

Critical pair: bbbbbbb=ba.

Reduce LHS:

[6](bbbbb)bb
⇒ bbb

Flip LHS and RHS.

Defines rule #2.