Certificate for #3431 ⟨a, b, c | ba=ab, cac=b⟩

Completion settings:

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

Axiom: ba=ab.

Flip LHS and RHS.

Referenced by [5].

Axiom: cac=b.

Referenced by [4].

Axiom: ac=d.

Defines rule #5.

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

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

Critical pair: cd=b.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

Simplify [1] ab=ba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7].

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

Critical pair: cdd=ddc.

Flip LHS and RHS.

Defines rule #1.

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

Critical pair: add=dda.

Flip LHS and RHS.

Defines rule #3.