Certificate for #5377 ⟨a, b | ababbba=bbaa⟩

Completion settings:

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

Axiom: ababbba=bbaa.

Referenced by [3].

Axiom: bbaa=c.

Defines rule #1.

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

Simplify [1] ababbba=bbaa.

Reduce RHS:

Defines rule #4.

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

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

Critical pair: ababbbc=cbabbba.

Referenced by [7], [9].

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

Critical pair: ababc=ca.

Defines rule #2.

Referenced by [7].

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

Critical pair: bbac=cbabbba.

Flip LHS and RHS.

Defines rule #5.

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

Overlap of [3] ababbba=c with [5] ababc=ca:

Critical pair: ababbbca=cbabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] cbabbba=bbac with [3] ababbba=c:

Critical pair: cbabbbc=bbacbabbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Simplify [4] ababbbc=cbabbba.

Reduce RHS:

Defines rule #6.

Referenced by [10], [11].

Overlap of [3] ababbba=c with [9] ababbbc=bbac:

Critical pair: ababbbbbac=cbabbbc.

Defines rule #8.

Overlap of [6] cbabbba=bbac with [9] ababbbc=bbac:

Critical pair: cbabbbbbac=bbacbabbbc.

Defines rule #9.