Certificate for #5287 ⟨a, b | abaaaab=abba⟩

Completion settings:

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

Axiom: abaaaab=abba.

Referenced by [3].

Axiom: abba=c.

Defines rule #1.

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

Simplify [1] abaaaab=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] abaaaab=c with [3] abaaaab=c:

Critical pair: abaaac=caaaab.

Flip LHS and RHS.

Referenced by [13].

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

Critical pair: abaaac=cba.

Defines rule #4.

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

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

Critical pair: abbc=cbaaaab.

Flip LHS and RHS.

Defines rule #8.

Overlap of [3] abaaaab=c with [6] abaaac=cba:

Critical pair: abaaacba=caaac.

Reduce LHS:

Defines rule #3.

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

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

Critical pair: abbcba=cbaaac.

Flip LHS and RHS.

Defines rule #6.

Overlap of [6] abaaac=cba with [8] cbaba=caaac:

Critical pair: abaaacaaac=cbababa.

Reduce LHS:

Reduce RHS:

Defines rule #9.

Overlap of [8] cbaba=caaac with [3] abaaaab=c:

Critical pair: cbc=caaacaaab.

Flip LHS and RHS.

Defines rule #12.

Overlap of [8] cbaba=caaac with [6] abaaac=cba:

Critical pair: cbcba=caaacaac.

Flip LHS and RHS.

Defines rule #10.

Simplify [5] caaaab=abaaac.

Reduce RHS:

Defines rule #5.

Referenced by [14].

Overlap of [13] caaaab=cba with [3] abaaaab=c:

Critical pair: caaac=cbaaaaab.

Flip LHS and RHS.

Defines rule #11.