Certificate for #6068 ⟨a, b, c | ab=c, bac=ba⟩

Completion settings:

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

Axiom: ab=c.

Defines rule #2.

Referenced by [5], [6], [9], [11].

Axiom: bac=ba.

Referenced by [4].

Axiom: ac=d.

Defines rule #3.

Referenced by [4], [7], [8], [10], [12].

Overlap of [2] bac=ba with [3] ac=d:

Critical pair: bd=ba.

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [1] ab=c with [4] ba=bd:

Critical pair: abd=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9], [10].

Overlap of [4] ba=bd with [1] ab=c:

Critical pair: bc=bdb.

Flip LHS and RHS.

Defines rule #8.

Overlap of [4] ba=bd with [3] ac=d:

Critical pair: bd=bdc.

Flip LHS and RHS.

Defines rule #9.

Overlap of [3] ac=d with [5] ca=cd:

Critical pair: acd=da.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [11], [12].

Overlap of [5] ca=cd with [1] ab=c:

Critical pair: cc=cdb.

Flip LHS and RHS.

Defines rule #10.

Overlap of [5] ca=cd with [3] ac=d:

Critical pair: cd=cdc.

Flip LHS and RHS.

Defines rule #11.

Overlap of [8] da=dd with [1] ab=c:

Critical pair: dc=ddb.

Flip LHS and RHS.

Defines rule #6.

Overlap of [8] da=dd with [3] ac=d:

Critical pair: dd=ddc.

Flip LHS and RHS.

Defines rule #7.