Certificate for #3338 ⟨a, b, c | ab=aa, bca=c⟩

Back:⟨a, b, c | ab=aa, bca=c⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bca=c

Axiom: bca=c.

Defines rule #3.

Referenced by [3], [4], [5], [6].

[3] aaca=ac

Overlap of [1] ab=aa with [2] bca=c:

a b bca

Critical pair: ac=aaca.

Flip LHS and RHS.

Defines rule #5.

[4] cb=ca

Overlap of [2] bca=c with [1] ab=aa:

bc a ab

Critical pair: bcaa=cb.

Reduce LHS:

[2](bca)a
⇒ ca

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] caca=cc

Overlap of [4] cb=ca with [2] bca=c:

c b bca

Critical pair: cc=caca.

Flip LHS and RHS.

Defines rule #6.

Referenced by [6].

[6] cca=bcc

Overlap of [2] bca=c with [5] caca=cc:

b ca caca

Critical pair: bcc=cca.

Flip LHS and RHS.

Defines rule #4.