Certificate for #13234 ⟨a, b | baa=abb, bab=ba⟩

Completion settings:

[1] baa=abb

Axiom: baa=abb.

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

[2] bab=ba

Axiom: bab=ba.

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

[3] abbb=abb

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

ba b bab

Critical pair: baba=baab.

Reduce LHS:

[2](bab)a
[1]⇒ (baa)
⇒ abb

Reduce RHS:

[1](baa)b
⇒ abbb

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [6].

[4] abba=abb

Overlap of [2] bab=ba with [1] baa=abb:

ba b baa

Critical pair: baabb=baaa.

Reduce LHS:

[1](baa)bb
[3]⇒ (abbb)b
[3]⇒ (abbb)
⇒ abb

Reduce RHS:

[1](baa)a
⇒ abba

Flip LHS and RHS.

Referenced by [5], [6].

[5] ba=abb

Overlap of [2] bab=ba with [4] abba=abb:

b ab abba

Critical pair: babb=baba.

Reduce LHS:

[2](bab)b
[2]⇒ (bab)
⇒ ba

Reduce RHS:

[2](bab)a
[1]⇒ (baa)
⇒ abb

Defines rule #2.

Referenced by [6].

[6] aabb=abb

Overlap of [4] abba=abb with [1] baa=abb:

ab ba baa

Critical pair: ababb=abba.

Reduce LHS:

[5]a(ba)bb
[3]⇒ a(abbb)b
[3]⇒ a(abbb)
⇒ aabb

Reduce RHS:

[4](abba)
⇒ abb

Defines rule #3.