Certificate for #4269 ⟨a, b, c | aab=1, bcba=c⟩

Back:⟨a, b, c | aab=1, bcba=c⟩

Completion settings:

[1] aab=1

Axiom: aab=1.

Defines rule #2.

Referenced by [3], [4].

[2] bcba=c

Axiom: bcba=c.

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

[3] aac=cba

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

aa b bcba

Critical pair: aac=cba.

Defines rule #1.

[4] bcb=cab

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

bcb a aab

Critical pair: bcb=cab.

Defines rule #4.

Referenced by [5], [6].

[5] caba=c

Overlap of [2] bcba=c with [4] bcb=cab:

bcba bcb

Critical pair: caba=c.

Defines rule #5.

Referenced by [7].

[6] bccab=cacab

Overlap of [4] bcb=cab with [4] bcb=cab:

bc b bcb

Critical pair: bccab=cabcb.

Reduce RHS:

[4]ca(bcb)
⇒ cacab

Referenced by [7].

[7] bcc=cac

Overlap of [6] bccab=cacab with [5] caba=c:

bc cab caba

Critical pair: bcc=cacaba.

Reduce RHS:

[5]ca(caba)
⇒ cac

Defines rule #3.