Certificate for #12365 ⟨a, b | aaba=ab, baab=b⟩

Back:⟨a, b | aaba=ab, baab=b⟩

Completion settings:

[1] aaba=ab

Axiom: aaba=ab.

Referenced by [3], [5].

[2] baab=b

Axiom: baab=b.

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

[3] bab=ba

Overlap of [2] baab=b with [1] aaba=ab:

b aab aaba

Critical pair: bab=ba.

Defines rule #2.

Referenced by [4].

[4] baa=b

Overlap of [3] bab=ba with [3] bab=ba:

ba b bab

Critical pair: baba=baab.

Reduce LHS:

[3](bab)a
⇒ baa

Reduce RHS:

[2](baab)
⇒ b

Defines rule #3.

Referenced by [5], [6].

[5] aab=aba

Overlap of [1] aaba=ab with [4] baa=b:

aa ba baa

Critical pair: aab=aba.

Defines rule #4.

[6] bb=b

Overlap of [2] baab=b with [4] baa=b:

baab baa

Critical pair: bb=b.

Defines rule #1.