Certificate for #13258 ⟨a, b | bab=aba, bba=bb⟩

Back:⟨a, b | bab=aba, bba=bb⟩

Completion settings:

[1] aba=bab

Axiom: bab=aba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #1.

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

[3] abbb=babb

Overlap of [1] aba=bab with [1] aba=bab:

ab a aba

Critical pair: abbab=babba.

Reduce LHS:

[2]a(bba)b
⇒ abbb

Reduce RHS:

[2]ba(bba)
⇒ babb

Referenced by [5], [6].

[4] bbbb=bbb

Overlap of [2] bba=bb with [1] aba=bab:

bb a aba

Critical pair: bbbab=bbba.

Reduce LHS:

[2]b(bba)b
⇒ bbbb

Reduce RHS:

[2]b(bba)
⇒ bbb

Defines rule #3.

Referenced by [5].

[5] babb=bbb

Overlap of [3] abbb=babb with [4] bbbb=bbb:

a bbb bbbb

Critical pair: abbb=babbb.

Reduce LHS:

[3](abbb)
⇒ babb

Reduce RHS:

[3]b(abbb)
[2]⇒ (bba)bb
[4]⇒ (bbbb)
⇒ bbb

Defines rule #4.

Referenced by [6].

[6] abbb=bbb

Simplify [3] abbb=babb.

Reduce RHS:

[5](babb)
⇒ bbb

Defines rule #5.