Certificate for #7486 ⟨a, b, c | ab=1, baca=ac⟩

Completion settings:

• Auxiliary generators:
  1. d = ac
  2. e = db
• Reduction order:
  • Left-to-right shortlex with d < a < b < e < c

Axiom: ab=1.

Defines rule #4.

Referenced by [7], [8], [10].

Axiom: baca=ac.

Referenced by [5].

Axiom: ac=d.

Defines rule #6.

Referenced by [5], [6], [9].

Axiom: db=e.

Defines rule #1.

Referenced by [8], [11], [13].

Simplify [2] baca=ac.

Reduce RHS:

Referenced by [6].

Overlap of [5] baca=d with [3] ac=d:

Critical pair: bda=d.

Referenced by [7], [8], [9], [12].

Overlap of [1] ab=1 with [6] bda=d:

Critical pair: ad=da.

Defines rule #3.

Overlap of [6] bda=d with [1] ab=1:

Critical pair: bd=db.

Reduce RHS:

Defines rule #7.

Referenced by [9], [10], [11], [12], [13], [14].

Overlap of [6] bda=d with [3] ac=d:

Critical pair: bdd=dc.

Reduce LHS:

Referenced by [11], [15].

Overlap of [1] ab=1 with [8] bd=e:

Critical pair: ae=d.

Defines rule #5.

Overlap of [4] db=e with [8] bd=e:

Critical pair: de=ed.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [14], [15].

Overlap of [6] bda=d with [8] bd=e:

Critical pair: ea=d.

Defines rule #9.

Overlap of [8] bd=e with [4] db=e:

Critical pair: be=eb.

Flip LHS and RHS.

Defines rule #10.

Overlap of [8] bd=e with [11] dc=de:

Critical pair: bde=ec.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Simplify [9] ed=dc.

Reduce RHS:

Defines rule #8.