Certificate for #5871 ⟨a, b | ababab=abbaa⟩

Completion settings:

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

Axiom: ababab=abbaa.

Flip LHS and RHS.

Referenced by [2], [3].

Axiom: abbaa=c.

Reduce LHS:

Defines rule #5.

Referenced by [3], [5], [6], [7].

Simplify [1] abbaa=ababab.

Reduce RHS:

Defines rule #6.

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

Overlap of [3] abbaa=c with [3] abbaa=c:

Critical pair: abbac=cbbaa.

Flip LHS and RHS.

Defines rule #4.

Overlap of [3] abbaa=c with [2] ababab=c:

Critical pair: abbac=cbabab.

Flip LHS and RHS.

Defines rule #3.

Overlap of [2] ababab=c with [3] abbaa=c:

Critical pair: ababc=cbaa.

Flip LHS and RHS.

Defines rule #2.

Overlap of [2] ababab=c with [2] ababab=c:

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #1.