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 #1.

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

[2] bab=ba

Axiom: bab=ba.

Defines rule #2.

Referenced by [3], [5].

[3] bbb=baa

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

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

[4] bbaa=baa

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

aa b bbb

Critical pair: aabaa=bbbb.

Reduce LHS:

[1](aab)aa
⇒ bbaa

Reduce RHS:

[3](bbb)b
[1]⇒ b(aab)
[3]⇒ (bbb)
⇒ baa

Referenced by [6].

[5] baaa=ba

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

ba b bbb

Critical pair: babaa=babb.

Reduce LHS:

[2](bab)aa
⇒ baaa

Reduce RHS:

[2](bab)b
[2]⇒ (bab)
⇒ ba

Defines rule #5.

Referenced by [6].

[6] bba=ba

Overlap of [1] aab=bb with [5] baaa=ba:

aa b baaa

Critical pair: aaba=bbaaa.

Reduce LHS:

[1](aab)a
⇒ bba

Reduce RHS:

[4](bbaa)a
[5]⇒ (baaa)
⇒ ba

Defines rule #3.