Certificate for #4275 ⟨a, b, c | aab=1, bcbc=c⟩

Back:⟨a, b, c | aab=1, bcbc=c⟩

Completion settings:

[1] aab=1

Axiom: aab=1.

Defines rule #1.

Referenced by [3].

[2] bcbc=c

Axiom: bcbc=c.

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

[3] cbc=aac

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

aa b bcbc

Critical pair: aac=cbc.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aac=bcc

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

bc bc bcbc

Critical pair: bcc=cbc.

Reduce RHS:

[3](cbc)
⇒ aac

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] cbc=bcc

Simplify [3] cbc=aac.

Reduce RHS:

[4](aac)
⇒ bcc

Defines rule #3.

Referenced by [6].

[6] bbcc=c

Overlap of [2] bcbc=c with [5] cbc=bcc:

b cbc cbc

Critical pair: bbcc=c.

Defines rule #4.