Certificate for #5194 ⟨a, b | aababba=aabb⟩

Completion settings:

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

Axiom: aababba=aabb.

Referenced by [3].

Axiom: aabb=c.

Defines rule #1.

Referenced by [3], [5].

Simplify [1] aababba=aabb.

Reduce RHS:

Defines rule #2.

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

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

Critical pair: aababbc=cababba.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: aababbc=cabb.

Defines rule #3.

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

Overlap of [3] aababba=c with [5] aababbc=cabb:

Critical pair: aababbcabb=cababbc.

Reduce LHS:

Defines rule #5.

Simplify [4] cababba=aababbc.

Reduce RHS:

Defines rule #4.

Referenced by [8], [9].

Overlap of [7] cababba=cabb with [3] aababba=c:

Critical pair: cababbc=cabbababba.

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] cababba=cabb with [5] aababbc=cabb:

Critical pair: cababbcabb=cabbababbc.

Flip LHS and RHS.

Defines rule #7.