Certificate for #6992 ⟨a, b, c | ab=1, bacac=c⟩

Back:⟨a, b, c | ab=1, bacac=c⟩

Completion settings:

[1] ab=1

Axiom: ab=1.

Defines rule #1.

Referenced by [3].

[2] bacac=c

Axiom: bacac=c.

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

[3] acac=ac

Overlap of [1] ab=1 with [2] bacac=c:

a b bacac

Critical pair: ac=acac.

Flip LHS and RHS.

Referenced by [4], [5].

[4] cac=c

Overlap of [2] bacac=c with [3] acac=ac:

bac ac acac

Critical pair: bacac=cac.

Reduce LHS:

[2](bacac)
⇒ c

Flip LHS and RHS.

Defines rule #3.

[5] bac=c

Overlap of [2] bacac=c with [3] acac=ac:

b acac acac

Critical pair: bac=c.

Defines rule #2.