Certificate for #5355 ⟨a, b | aab=aa, aba=ba⟩

Back:⟨a, b | aab=aa, aba=ba⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #3.

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

[2] aba=ba

Axiom: aba=ba.

Referenced by [3], [5].

[3] ba=aaa

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

a ab aba

Critical pair: aba=aaa.

Reduce LHS:

[2](aba)
⇒ ba

Defines rule #2.

Referenced by [4], [5].

[4] aaaaa=aaa

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

aa b ba

Critical pair: aaaaa=aaa.

Referenced by [5].

[5] aaaa=aaa

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

b a aba

Critical pair: bba=aaaba.

Reduce LHS:

[3]b(ba)
[3]⇒ (ba)aa
[4]⇒ (aaaaa)
⇒ aaa

Reduce RHS:

[1]a(aab)a
⇒ aaaa

Flip LHS and RHS.

Defines rule #1.