Certificate for #5368 ⟨a, b | ababbba=aabb⟩

Completion settings:

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

Axiom: ababbba=aabb.

Referenced by [3].

Axiom: aabb=c.

Defines rule #1.

Referenced by [3], [5].

Simplify [1] ababbba=aabb.

Reduce RHS:

Defines rule #2.

Referenced by [4], [5], [6], [8].

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

Critical pair: ababbbc=cbabbba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] ababbba=c with [2] aabb=c:

Critical pair: ababbbc=cabb.

Defines rule #3.

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

Overlap of [3] ababbba=c with [5] ababbbc=cabb:

Critical pair: ababbbcabb=cbabbbc.

Reduce LHS:

Defines rule #5.

Simplify [4] cbabbba=ababbbc.

Reduce RHS:

Defines rule #4.

Referenced by [8], [9].

Overlap of [7] cbabbba=cabb with [3] ababbba=c:

Critical pair: cbabbbc=cabbbabbba.

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] cbabbba=cabb with [5] ababbbc=cabb:

Critical pair: cbabbbcabb=cabbbabbbc.

Flip LHS and RHS.

Defines rule #7.