Certificate for #3011 ⟨a, b, c | aba=a, aca=c⟩

Back:⟨a, b, c | aba=a, aca=c⟩

Completion settings:

[1] aba=a

Axiom: aba=a.

Defines rule #1.

Referenced by [3], [4].

[2] aca=c

Axiom: aca=c.

Defines rule #3.

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

[3] abc=c

Overlap of [1] aba=a with [2] aca=c:

ab a aca

Critical pair: abc=aca.

Reduce RHS:

[2](aca)
⇒ c

Defines rule #2.

Referenced by [6].

[4] cba=c

Overlap of [2] aca=c with [1] aba=a:

ac a aba

Critical pair: aca=cba.

Reduce LHS:

[2](aca)
⇒ c

Flip LHS and RHS.

Defines rule #4.

[5] cca=acc

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

ac a aca

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #6.

[6] cbc=acc

Overlap of [2] aca=c with [3] abc=c:

ac a abc

Critical pair: acc=cbc.

Flip LHS and RHS.

Defines rule #5.