Certificate for #6824 ⟨a, b | aab=b, bbb=aaa⟩

Back:⟨a, b | aab=b, bbb=aaa⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Referenced by [3], [5].

[2] aaa=bbb

Axiom: bbb=aaa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[3] ab=bbbb

Overlap of [2] aaa=bbb with [1] aab=b:

a aa aab

Critical pair: ab=bbbb.

Defines rule #2.

Referenced by [4], [5].

[4] bbba=bbbbbb

Overlap of [2] aaa=bbb with [2] aaa=bbb:

a aa aaa

Critical pair: abbb=bbba.

Reduce LHS:

[3](ab)bb
⇒ bbbbbb

Flip LHS and RHS.

Referenced by [6].

[5] bbbbbbb=b

Overlap of [1] aab=b with [3] ab=bbbb:

a ab ab

Critical pair: abbbb=b.

Reduce LHS:

[3](ab)bbb
⇒ bbbbbbb

Defines rule #1.

Referenced by [6].

[6] ba=bbbb

Overlap of [5] bbbbbbb=b with [4] bbba=bbbbbb:

bbbb bbb bbba

Critical pair: bbbbbbbbbb=ba.

Reduce LHS:

[5](bbbbbbb)bbb
⇒ bbbb

Flip LHS and RHS.

Defines rule #3.