Certificate for #5328 ⟨a, b | abaabba=abab⟩

Completion settings:

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

Axiom: abaabba=abab.

Referenced by [3].

Axiom: abab=c.

Defines rule #2.

Referenced by [3], [4], [6], [7], [8].

Simplify [1] abaabba=abab.

Reduce RHS:

Defines rule #5.

Referenced by [5], [6], [7], [9], [11].

Overlap of [2] abab=c with [2] abab=c:

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #1.

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

Critical pair: abaabbc=cbaabba.

Flip LHS and RHS.

Referenced by [10].

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

Critical pair: abaabbc=cbab.

Defines rule #6.

Referenced by [9], [10], [12].

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

Critical pair: abc=caabba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [7] caabba=abc with [2] abab=c:

Critical pair: caabbc=abcbab.

Defines rule #4.

Overlap of [3] abaabba=c with [6] abaabbc=cbab:

Critical pair: abaabbcbab=cbaabbc.

Reduce LHS:

Defines rule #8.

Simplify [5] cbaabba=abaabbc.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [10] cbaabba=cbab with [3] abaabba=c:

Critical pair: cbaabbc=cbabbaabba.

Flip LHS and RHS.

Defines rule #9.

Overlap of [10] cbaabba=cbab with [6] abaabbc=cbab:

Critical pair: cbaabbcbab=cbabbaabbc.

Flip LHS and RHS.

Defines rule #10.