Certificate for #1659 ⟨a, b, c | aab=ba, aca=1⟩

Back:⟨a, b, c | aab=ba, aca=1⟩

Completion settings:

[1] aab=ba

Axiom: aab=ba.

Defines rule #4.

Referenced by [4].

[2] aca=1

Axiom: aca=1.

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

[3] ca=ac

Overlap of [2] aca=1 with [2] aca=1:

ac a aca

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

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

[4] cba=b

Overlap of [3] ca=ac with [1] aab=ba:

c a aab

Critical pair: cba=acab.

Reduce RHS:

[2](aca)b
⇒ b

Referenced by [5].

[5] cb=bac

Overlap of [4] cba=b with [2] aca=1:

cb a aca

Critical pair: cb=bca.

Reduce RHS:

[3]b(ca)
⇒ bac

Defines rule #3.

[6] aac=1

Overlap of [2] aca=1 with [3] ca=ac:

a ca ca

Critical pair: aac=1.

Defines rule #2.