Certificate for #5335 ⟨a, b | abaabba=bbaa⟩

Completion settings:

• Reduction order:
  • Right-to-left shortlex with b < a < c
• Auxiliary generators:
  1. bbaa=c

Axiom: abaabba=bbaa.

Referenced by [3].

Axiom: bbaa=c.

Defines rule #1.

Referenced by [3], [5], [6].

Simplify [1] abaabba=bbaa.

Reduce RHS:

Defines rule #4.

Referenced by [4], [5], [6], [7], [8], [10].

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

Critical pair: abaabbc=cbaabba.

Referenced by [7], [9].

Overlap of [3] abaabba=c with [2] bbaa=c:

Critical pair: abaac=ca.

Defines rule #2.

Referenced by [7].

Overlap of [2] bbaa=c with [3] abaabba=c:

Critical pair: bbac=cbaabba.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8], [9], [11].

Overlap of [3] abaabba=c with [5] abaac=ca:

Critical pair: abaabbca=cbaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] cbaabba=bbac with [3] abaabba=c:

Critical pair: cbaabbc=bbacbaabba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Simplify [4] abaabbc=cbaabba.

Reduce RHS:

Defines rule #6.

Referenced by [10], [11].

Overlap of [3] abaabba=c with [9] abaabbc=bbac:

Critical pair: abaabbbbac=cbaabbc.

Defines rule #8.

Overlap of [6] cbaabba=bbac with [9] abaabbc=bbac:

Critical pair: cbaabbbbac=bbacbaabbc.

Defines rule #9.