Certificate for #5313 ⟨a, b | abaabab=abba⟩

Completion settings:

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

Axiom: abaabab=abba.

Referenced by [3].

Axiom: abba=c.

Defines rule #1.

Referenced by [3], [4], [6], [7], [9].

Simplify [1] abaabab=abba.

Reduce RHS:

Defines rule #7.

Referenced by [5], [6], [7], [8], [11], [14].

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

Critical pair: abbc=cbba.

Flip LHS and RHS.

Defines rule #2.

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

Critical pair: abaabc=caabab.

Flip LHS and RHS.

Referenced by [13].

Overlap of [3] abaabab=c with [2] abba=c:

Critical pair: abaabc=cba.

Defines rule #4.

Referenced by [8], [9], [10], [12], [13].

Overlap of [2] abba=c with [3] abaabab=c:

Critical pair: abbc=cbaabab.

Flip LHS and RHS.

Defines rule #9.

Overlap of [3] abaabab=c with [6] abaabc=cba:

Critical pair: abaabcba=caabc.

Reduce LHS:

Defines rule #3.

Referenced by [10], [11], [12].

Overlap of [2] abba=c with [6] abaabc=cba:

Critical pair: abbcba=cbaabc.

Flip LHS and RHS.

Defines rule #6.

Overlap of [6] abaabc=cba with [8] cbaba=caabc:

Critical pair: abaabcaabc=cbababa.

Reduce LHS:

Reduce RHS:

Defines rule #8.

Overlap of [8] cbaba=caabc with [3] abaabab=c:

Critical pair: cbc=caabcabab.

Flip LHS and RHS.

Defines rule #12.

Overlap of [8] cbaba=caabc with [6] abaabc=cba:

Critical pair: cbcba=caabcabc.

Flip LHS and RHS.

Defines rule #10.

Simplify [5] caabab=abaabc.

Reduce RHS:

Defines rule #5.

Referenced by [14].

Overlap of [13] caabab=cba with [3] abaabab=c:

Critical pair: caabc=cbaaabab.

Flip LHS and RHS.

Defines rule #11.