Certificate for #974 ⟨a, b, c | ab=a, bca=c⟩

Back:⟨a, b, c | ab=a, bca=c⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bca=c

Axiom: bca=c.

Defines rule #4.

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

[3] aca=ac

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

a b bca

Critical pair: ac=aca.

Flip LHS and RHS.

Defines rule #3.

[4] cb=c

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

bc a ab

Critical pair: bca=cb.

Reduce LHS:

[2](bca)
⇒ c

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] cca=cc

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

c b bca

Critical pair: cc=cca.

Flip LHS and RHS.

Defines rule #5.