Certificate for #2569 ⟨a, b | abaaab=abba⟩

Completion settings:

• Auxiliary generators:
  1. c = abba
• Reduction order:
  • Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1

Axiom: abaaab=abba.

Referenced by [3].

Axiom: abba=c.

Defines rule #2.

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

Simplify [1] abaaab=abba.

Reduce RHS:

Defines rule #10.

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 #1.

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

Critical pair: abaac=caaab.

Flip LHS and RHS.

Referenced by [13].

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

Critical pair: abaac=cba.

Defines rule #5.

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

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

Critical pair: abbc=cbaaab.

Flip LHS and RHS.

Defines rule #8.

Overlap of [3] abaaab=c with [6] abaac=cba:

Critical pair: abaacba=caac.

Reduce LHS:

Defines rule #4.

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

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

Critical pair: abbcba=cbaac.

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] abaac=cba with [8] cbaba=caac:

Critical pair: abaacaac=cbababa.

Reduce LHS:

Reduce RHS:

Defines rule #9.

Overlap of [8] cbaba=caac with [3] abaaab=c:

Critical pair: cbc=caacaab.

Flip LHS and RHS.

Defines rule #11.

Overlap of [8] cbaba=caac with [6] abaac=cba:

Critical pair: cbcba=caacac.

Flip LHS and RHS.

Defines rule #7.

Simplify [5] caaab=abaac.

Reduce RHS:

Defines rule #6.

Referenced by [14].

Overlap of [13] caaab=cba with [3] abaaab=c:

Critical pair: caac=cbaaaab.

Flip LHS and RHS.

Defines rule #12.