Certificate for #6546 ⟨a, b | aaa=a, abba=ab⟩

Back:⟨a, b | aaa=a, abba=ab⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #1.

Referenced by [3].

[2] abba=ab

Axiom: abba=ab.

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

[3] abaa=ab

Overlap of [2] abba=ab with [1] aaa=a:

abb a aaa

Critical pair: abba=abaa.

Reduce LHS:

[2](abba)
⇒ ab

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[4] abb=aba

Overlap of [2] abba=ab with [3] abaa=ab:

abb a abaa

Critical pair: abbab=abbaa.

Reduce LHS:

[2](abba)b
⇒ abb

Reduce RHS:

[2](abba)a
⇒ aba

Defines rule #2.

Referenced by [5].

[5] abab=ab

Overlap of [2] abba=ab with [4] abb=aba:

abb a abb

Critical pair: abbaba=abbb.

Reduce LHS:

[4](abb)aba
[3]⇒ (abaa)ba
[4]⇒ (abb)a
[3]⇒ (abaa)
⇒ ab

Reduce RHS:

[4](abb)b
⇒ abab

Flip LHS and RHS.

Defines rule #4.