Certificate for #5412 ⟨a, b | aab=bb, bab=ba⟩

Back:⟨a, b | aab=bb, bab=ba⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #4.

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

[2] bab=ba

Axiom: bab=ba.

Defines rule #2.

Referenced by [3], [4].

[3] baa=bbb

Overlap of [2] bab=ba with [2] bab=ba:

ba b bab

Critical pair: baba=baab.

Reduce LHS:

[2](bab)a
⇒ baa

Reduce RHS:

[1]b(aab)
⇒ bbb

Defines rule #3.

Referenced by [4], [5].

[4] bbba=ba

Overlap of [2] bab=ba with [3] baa=bbb:

ba b baa

Critical pair: babbb=baaa.

Reduce LHS:

[2](bab)bb
[2]⇒ (bab)b
[2]⇒ (bab)
⇒ ba

Reduce RHS:

[3](baa)a
⇒ bbba

Flip LHS and RHS.

Referenced by [6].

[5] bbbb=bbb

Overlap of [3] baa=bbb with [1] aab=bb:

b aa aab

Critical pair: bbb=bbbb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [6].

[6] bba=ba

Overlap of [1] aab=bb with [4] bbba=ba:

aa b bbba

Critical pair: aaba=bbbba.

Reduce LHS:

[1](aab)a
⇒ bba

Reduce RHS:

[5](bbbb)a
[4]⇒ (bbba)
⇒ ba

Defines rule #1.