Certificate for #6443 ⟨a, b | aab=b, bbbba=b⟩

Back:⟨a, b | aab=b, bbbba=b⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3].

[2] bbbba=b

Axiom: bbbba=b.

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

[3] bab=bbbbb

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

bbbb a aab

Critical pair: bbbbb=bab.

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbbbbbbb=bb

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

bbb ba bab

Critical pair: bbbbbbbb=bb.

Referenced by [5].

[5] bba=bbbbb

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

ba b bbbba

Critical pair: bab=bbbbbbbba.

Reduce LHS:

[3](bab)
⇒ bbbbb

Reduce RHS:

[4](bbbbbbbb)a
⇒ bba

Flip LHS and RHS.

Referenced by [6], [7].

[6] bbbbbbb=b

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

bb bba bba

Critical pair: bbbbbbb=b.

Defines rule #1.

Referenced by [7].

[7] ba=bbbb

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

bbbbb bb bba

Critical pair: bbbbbbbbbb=ba.

Reduce LHS:

[6](bbbbbbb)bbb
⇒ bbbb

Flip LHS and RHS.

Defines rule #2.