Certificate for #2619 ⟨a, b | abbaab=abaa⟩

Completion settings:

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

Axiom: abbaab=abaa.

Referenced by [3].

Axiom: abaa=c.

Defines rule #7.

Referenced by [3], [4], [6], [7], [9].

Simplify [1] abbaab=abaa.

Reduce RHS:

Defines rule #8.

Referenced by [5], [6], [7], [8].

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

Critical pair: abac=cbaa.

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [8].

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

Critical pair: abbac=cbaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [9].

Overlap of [3] abbaab=c with [2] abaa=c:

Critical pair: abbac=caa.

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] abaa=c with [3] abbaab=c:

Critical pair: abac=cbbaab.

Flip LHS and RHS.

Defines rule #6.

Overlap of [4] cbaa=abac with [3] abbaab=c:

Critical pair: cbac=abacbbaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] abaa=c with [5] abacb=abbac:

Critical pair: abaabbac=cbacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.