Certificate for #1320 ⟨a, b, c | ab=1, acba=c⟩

Back:⟨a, b, c | ab=1, acba=c⟩

Completion settings:

[1] ab=1

Axiom: ab=1.

Defines rule #1.

Referenced by [3].

[2] acba=c

Axiom: acba=c.

Referenced by [3], [4], [6].

[3] acb=cb

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

acb a ab

Critical pair: acb=cb.

Referenced by [4], [5].

[4] cba=c

Overlap of [2] acba=c with [3] acb=cb:

acba acb

Critical pair: cba=c.

Defines rule #3.

Referenced by [5].

[5] ac=c

Overlap of [3] acb=cb with [4] cba=c:

a cb cba

Critical pair: ac=cba.

Reduce RHS:

[4](cba)
⇒ c

Defines rule #2.

Referenced by [6].

[6] cbc=cc

Overlap of [2] acba=c with [5] ac=c:

acb a ac

Critical pair: acbc=cc.

Reduce LHS:

[5](ac)bc
⇒ cbc

Defines rule #4.