Certificate for #2602 ⟨a, b | ababba=aabb⟩

Completion settings:

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

Axiom: ababba=aabb.

Referenced by [3].

Axiom: aabb=c.

Defines rule #1.

Referenced by [3], [5].

Simplify [1] ababba=aabb.

Reduce RHS:

Defines rule #2.

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

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

Critical pair: ababbc=cbabba.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: ababbc=cabb.

Defines rule #3.

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

Overlap of [3] ababba=c with [5] ababbc=cabb:

Critical pair: ababbcabb=cbabbc.

Reduce LHS:

Defines rule #5.

Simplify [4] cbabba=ababbc.

Reduce RHS:

Defines rule #4.

Referenced by [8], [9].

Overlap of [7] cbabba=cabb with [3] ababba=c:

Critical pair: cbabbc=cabbbabba.

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] cbabba=cabb with [5] ababbc=cabb:

Critical pair: cbabbcabb=cabbbabbc.

Flip LHS and RHS.

Defines rule #7.