Certificate for #2883 ⟨a, b, c | aab=a, bca=c⟩

Back:⟨a, b, c | aab=a, bca=c⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bca=c

Axiom: bca=c.

Defines rule #4.

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

[3] aca=aac

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

aa b bca

Critical pair: aac=aca.

Flip LHS and RHS.

Defines rule #3.

[4] cab=c

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

bc a aab

Critical pair: bca=cab.

Reduce LHS:

[2](bca)
⇒ c

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6].

[5] cb=bc

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

b ca cab

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #1.

[6] cca=cac

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

ca b bca

Critical pair: cac=cca.

Flip LHS and RHS.

Defines rule #6.