Certificate for #1364 ⟨a, b, c | ab=1, bcbc=c⟩

Back:⟨a, b, c | ab=1, bcbc=c⟩

Completion settings:

[1] ab=1

Axiom: ab=1.

Defines rule #3.

Referenced by [3].

[2] bcbc=c

Axiom: bcbc=c.

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

[3] ac=cbc

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

a b bcbc

Critical pair: ac=cbc.

Referenced by [5].

[4] cbc=bcc

Overlap of [2] bcbc=c with [2] bcbc=c:

bc bc bcbc

Critical pair: bcc=cbc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [5], [6].

[5] ac=bcc

Simplify [3] ac=cbc.

Reduce RHS:

[4](cbc)
⇒ bcc

Defines rule #4.

[6] bbcc=c

Overlap of [2] bcbc=c with [4] cbc=bcc:

b cbc cbc

Critical pair: bbcc=c.

Defines rule #2.