Certificate for #13055 ⟨a, b | baa=aab, abba=b⟩

Back:⟨a, b | baa=aab, abba=b⟩

Completion settings:

[1] baa=aab

Axiom: baa=aab.

Defines rule #1.

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

[2] abba=b

Axiom: abba=b.

Defines rule #2.

Referenced by [3], [4].

[3] bbba=abbb

Overlap of [2] abba=b with [2] abba=b:

abb a abba

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #4.

[4] aaabb=ba

Overlap of [2] abba=b with [1] baa=aab:

ab ba baa

Critical pair: abaab=ba.

Reduce LHS:

[1]a(baa)b
⇒ aaabb

Defines rule #5.

Referenced by [5], [6].

[5] aababb=bba

Overlap of [1] baa=aab with [4] aaabb=ba:

b aa aaabb

Critical pair: bba=aababb.

Flip LHS and RHS.

Defines rule #6.

[6] baba=abab

Overlap of [1] baa=aab with [4] aaabb=ba:

ba a aaabb

Critical pair: baba=aabaabb.

Reduce RHS:

[1]aa(baa)bb
[4]⇒ a(aaabb)b
⇒ abab

Defines rule #3.