Certificate for #5823 ⟨a, b | abaaab=abbba⟩

Completion settings:

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

Axiom: abaaab=abbba.

Referenced by [3].

Axiom: abbba=c.

Defines rule #2.

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

Simplify [1] abaaab=abbba.

Reduce RHS:

Defines rule #9.

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

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

Critical pair: abbbc=cbbba.

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 [10].

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

Critical pair: abaac=cbba.

Defines rule #5.

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

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

Critical pair: abbbc=cbaaab.

Flip LHS and RHS.

Defines rule #7.

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

Critical pair: abaacbba=caac.

Reduce LHS:

Defines rule #4.

Overlap of [2] abbba=c with [6] abaac=cbba:

Critical pair: abbbcbba=cbaac.

Flip LHS and RHS.

Defines rule #3.

Simplify [5] caaab=abaac.

Reduce RHS:

Defines rule #6.

Referenced by [11], [12].

Overlap of [10] caaab=cbba with [3] abaaab=c:

Critical pair: caac=cbbaaaab.

Flip LHS and RHS.

Defines rule #10.

Overlap of [10] caaab=cbba with [6] abaac=cbba:

Critical pair: caacbba=cbbaaac.

Flip LHS and RHS.

Defines rule #8.