Certificate for #6101 ⟨a, b, c | ab=c, cac=ba⟩

Completion settings:

• Auxiliary generators:
  1. d = ac
• Reduction order:
  • Right-to-left recursive path with deg(d) = 0; deg(b) = deg(c) = deg(a) = 1, b < c < a

Axiom: ab=c.

Defines rule #4.

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

Axiom: cac=ba.

Referenced by [4].

Axiom: ac=d.

Defines rule #7.

Referenced by [4], [5], [7], [8], [10].

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

Critical pair: cd=ba.

Flip LHS and RHS.

Referenced by [5], [6], [7], [13].

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

Critical pair: acd=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

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

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

Critical pair: bc=cdb.

Referenced by [11].

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

Critical pair: bd=cdc.

Flip LHS and RHS.

Referenced by [12].

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

Critical pair: add=da.

Defines rule #3.

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

Critical pair: cc=ddb.

Defines rule #6.

Referenced by [12].

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

Critical pair: cd=ddc.

Defines rule #2.

Referenced by [11], [12], [13].

Simplify [6] bc=cdb.

Reduce RHS:

Defines rule #5.

Simplify [7] cdc=bd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [4] ba=cd.

Reduce RHS:

Defines rule #8.