Certificate for #6702 ⟨a, b | aab=b, baba=aa⟩

Back:⟨a, b | aab=b, baba=aa⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #1.

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

[2] baba=aa

Axiom: baba=aa.

Defines rule #4.

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

[3] aaaa=aa

Overlap of [1] aab=b with [2] baba=aa:

aa b baba

Critical pair: aaaa=baba.

Reduce RHS:

[2](baba)
⇒ aa

Defines rule #2.

[4] babb=ab

Overlap of [2] baba=aa with [1] aab=b:

bab a aab

Critical pair: babb=aaab.

Reduce RHS:

[1]a(aab)
⇒ ab

Defines rule #5.

[5] baaa=ba

Overlap of [2] baba=aa with [2] baba=aa:

ba ba baba

Critical pair: baaa=aaba.

Reduce RHS:

[1](aab)a
⇒ ba

Defines rule #3.