Certificate for #1784 ⟨a, b | abababaab=b⟩

Back:⟨a, b | abababaab=b⟩

Completion settings:

[1] abababaab=b

Axiom: abababaab=b.

Referenced by [3].

[2] ab=c

Axiom: ab=c.

Referenced by [3], [4].

[3] b=cccac

Overlap of [1] abababaab=b with [2] ab=c:

abababaab ab

Critical pair: cababaab=b.

Reduce LHS:

[2]c(ab)abaab
[2]⇒ cc(ab)aab
[2]⇒ ccca(ab)
⇒ cccac

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] acccac=c

Overlap of [2] ab=c with [3] b=cccac:

a b b

Critical pair: acccac=c.

Defines rule #2.

Referenced by [5].

[5] acccc=cccac

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

accc ac acccac

Critical pair: acccc=cccac.

Defines rule #1.