Certificate for #5930 ⟨a, b, c | ab=a, cac=ca⟩

Back:⟨a, b, c | ab=a, cac=ca⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #4.

Referenced by [6].

[2] cac=ca

Axiom: cac=ca.

Referenced by [4].

[3] ca=d

Axiom: ca=d.

Defines rule #5.

Referenced by [4], [5], [6], [7].

[4] cac=d

Simplify [2] cac=ca.

Reduce RHS:

[3](ca)
⇒ d

Referenced by [5].

[5] dc=d

Overlap of [4] cac=d with [3] ca=d:

cac ca

Critical pair: dc=d.

Defines rule #3.

Referenced by [7].

[6] db=d

Overlap of [3] ca=d with [1] ab=a:

c a ab

Critical pair: ca=db.

Reduce LHS:

[3](ca)
⇒ d

Flip LHS and RHS.

Defines rule #2.

[7] da=dd

Overlap of [5] dc=d with [3] ca=d:

d c ca

Critical pair: dd=da.

Flip LHS and RHS.

Defines rule #1.