Certificate for #13122 ⟨a, b | aab=aaa, aba=ba⟩

Back:⟨a, b | aab=aaa, aba=ba⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #3.

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

[2] aba=ba

Axiom: aba=ba.

Referenced by [3], [5].

[3] ba=aaaa

Overlap of [1] aab=aaa with [2] aba=ba:

a ab aba

Critical pair: aba=aaaa.

Reduce LHS:

[2](aba)
⇒ ba

Defines rule #2.

Referenced by [4], [5].

[4] aaaaaa=aaaa

Overlap of [1] aab=aaa with [3] ba=aaaa:

aa b ba

Critical pair: aaaaaa=aaaa.

Referenced by [5].

[5] aaaaa=aaaa

Overlap of [3] ba=aaaa with [2] aba=ba:

b a aba

Critical pair: bba=aaaaba.

Reduce LHS:

[3]b(ba)
[3]⇒ (ba)aaa
[4]⇒ (aaaaaa)a
⇒ aaaaa

Reduce RHS:

[1]aa(aab)a
[4]⇒ (aaaaaa)
⇒ aaaa

Defines rule #1.