Certificate for #6534 ⟨a, b | aaa=a, aaba=ab⟩

Back:⟨a, b | aaa=a, aaba=ab⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #2.

Referenced by [6].

[2] aaba=ab

Axiom: aaba=ab.

Referenced by [4].

[3] ab=c

Axiom: ab=c.

Defines rule #4.

Referenced by [4], [5], [6], [7].

[4] aaba=c

Simplify [2] aaba=ab.

Reduce RHS:

[3](ab)
⇒ c

Referenced by [5].

[5] aca=c

Overlap of [4] aaba=c with [3] ab=c:

a aba ab

Critical pair: aca=c.

Referenced by [7], [8].

[6] aac=c

Overlap of [1] aaa=a with [3] ab=c:

aa a ab

Critical pair: aac=ab.

Reduce RHS:

[3](ab)
⇒ c

Defines rule #3.

Referenced by [8].

[7] cb=acc

Overlap of [5] aca=c with [3] ab=c:

ac a ab

Critical pair: acc=cb.

Flip LHS and RHS.

Defines rule #5.

[8] ca=ac

Overlap of [6] aac=c with [5] aca=c:

a ac aca

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.