Certificate for #930 ⟨a, b | aabaaba=ab⟩

Back:⟨a, b | aabaaba=ab⟩

Completion settings:

[1] aabaaba=ab

Axiom: aabaaba=ab.

Referenced by [3].

[2] ab=c

Axiom: ab=c.

Defines rule #3.

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

[3] aabaaba=c

Simplify [1] aabaaba=ab.

Reduce RHS:

[2](ab)
⇒ c

Referenced by [4].

[4] acaca=c

Overlap of [3] aabaaba=c with [2] ab=c:

a abaaba ab

Critical pair: acaaba=c.

Reduce LHS:

[2]aca(ab)a
⇒ acaca

Defines rule #2.

Referenced by [5], [6].

[5] cb=acacc

Overlap of [4] acaca=c with [2] ab=c:

acac a ab

Critical pair: acacc=cb.

Flip LHS and RHS.

Defines rule #4.

[6] cca=acc

Overlap of [4] acaca=c with [4] acaca=c:

ac aca acaca

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #1.