Certificate for #4840 ⟨a, b, c | ab=a, baacb=1⟩

Back:⟨a, b, c | ab=a, baacb=1⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] baacb=1

Axiom: baacb=1.

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

[3] aaacb=a

Overlap of [1] ab=a with [2] baacb=1:

a b baacb

Critical pair: a=aaacb.

Flip LHS and RHS.

Referenced by [5].

[4] baac=aacb

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

baac b baacb

Critical pair: baac=aacb.

Defines rule #3.

Referenced by [6].

[5] aaac=a

Overlap of [3] aaacb=a with [2] baacb=1:

aaac b baacb

Critical pair: aaac=aaacb.

Reduce RHS:

[3](aaacb)
⇒ a

Defines rule #2.

[6] aacbb=1

Overlap of [2] baacb=1 with [4] baac=aacb:

baacb baac

Critical pair: aacbb=1.

Defines rule #4.