Certificate for #2370 ⟨a, b, c | aab=a, bacb=1⟩

Back:⟨a, b, c | aab=a, bacb=1⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

Defines rule #1.

Referenced by [3], [5].

[2] bacb=1

Axiom: bacb=1.

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

[3] aacb=aa

Overlap of [1] aab=a with [2] bacb=1:

aa b bacb

Critical pair: aa=aacb.

Flip LHS and RHS.

Referenced by [5].

[4] bac=acb

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

bac b bacb

Critical pair: bac=acb.

Defines rule #3.

Referenced by [5], [6].

[5] aac=aaa

Overlap of [1] aab=a with [4] bac=acb:

aa b bac

Critical pair: aaacb=aac.

Reduce LHS:

[3]a(aacb)
⇒ aaa

Flip LHS and RHS.

Defines rule #2.

[6] acbb=1

Overlap of [2] bacb=1 with [4] bac=acb:

bacb bac

Critical pair: acbb=1.

Defines rule #4.