Certificate for #5403 ⟨a, b | abbabba=abbb⟩

Completion settings:

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

Axiom: abbabba=abbb.

Referenced by [3].

Axiom: abbb=c.

Defines rule #2.

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

Simplify [1] abbabba=abbb.

Reduce RHS:

Defines rule #7.

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

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

Critical pair: abbc=cbba.

Defines rule #1.

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

Overlap of [3] abbabba=c with [2] abbb=c:

Critical pair: abbabbc=cbbb.

Reduce LHS:

Defines rule #3.

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

Overlap of [3] abbabba=c with [4] abbc=cbba:

Critical pair: abbabbcbba=cbbc.

Reduce LHS:

Defines rule #5.

Overlap of [5] cbbabba=cbbb with [2] abbb=c:

Critical pair: cbbabbc=cbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] cbbabba=cbbb with [4] abbc=cbba:

Critical pair: cbbabbcbba=cbbbbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.