Certificate for #4411 ⟨a, b, c | aba=1, acbb=c⟩

Back:⟨a, b, c | aba=1, acbb=c⟩

Completion settings:

[1] aba=1

Axiom: aba=1.

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

[2] acbb=c

Axiom: acbb=c.

Referenced by [5], [6].

[3] ab=ba

Overlap of [1] aba=1 with [1] aba=1:

ab a aba

Critical pair: ab=ba.

Defines rule #1.

Referenced by [4], [5].

[4] baa=1

Overlap of [1] aba=1 with [3] ab=ba:

aba ab

Critical pair: baa=1.

Defines rule #2.

Referenced by [6].

[5] cbb=bac

Overlap of [1] aba=1 with [2] acbb=c:

ab a acbb

Critical pair: abc=cbb.

Reduce LHS:

[3](ab)c
⇒ bac

Flip LHS and RHS.

Defines rule #3.

[6] caa=acb

Overlap of [2] acbb=c with [4] baa=1:

acb b baa

Critical pair: acb=caa.

Flip LHS and RHS.

Defines rule #4.