Certificate for #16204 ⟨a, b | aab=ab, bbba=bb⟩

Back:⟨a, b | aab=ab, bbba=bb⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Defines rule #1.

Referenced by [3].

[2] bbba=bb

Axiom: bbba=bb.

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

[3] bbab=bbb

Overlap of [2] bbba=bb with [1] aab=ab:

bbb a aab

Critical pair: bbbab=bbab.

Reduce LHS:

[2](bbba)b
⇒ bbb

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbbb=bbb

Overlap of [2] bbba=bb with [3] bbab=bbb:

b bba bbab

Critical pair: bbbb=bbb.

Referenced by [5].

[5] bbb=bb

Overlap of [3] bbab=bbb with [2] bbba=bb:

bba b bbba

Critical pair: bbabb=bbbbba.

Reduce LHS:

[3](bbab)b
[4]⇒ (bbbb)
⇒ bbb

Reduce RHS:

[4](bbbb)ba
[4]⇒ (bbbb)a
[2]⇒ (bbba)
⇒ bb

Defines rule #3.

Referenced by [6].

[6] bba=bb

Overlap of [2] bbba=bb with [5] bbb=bb:

bbba bbb

Critical pair: bba=bb.

Defines rule #2.