Certificate for #3095 ⟨a, b, c | ab=aa, bacb=1⟩

Back:⟨a, b, c | ab=aa, bacb=1⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #2.

Referenced by [3], [5].

[2] bacb=1

Axiom: bacb=1.

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

[3] aaacb=a

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

a b bacb

Critical pair: a=aaacb.

Flip LHS and RHS.

Referenced by [5].

[4] acb=bac

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

bac b bacb

Critical pair: bac=acb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

[5] aaaac=a

Simplify [3] aaacb=a.

Reduce LHS:

[4]aa(acb)
[1]⇒ a(ab)ac
⇒ aaaac

Defines rule #1.

[6] bbac=1

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

b acb acb

Critical pair: bbac=1.

Defines rule #4.