Certificate for #2339 ⟨a, b | ababbba=baa⟩

Completion settings:

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

Axiom: ababbba=baa.

Referenced by [3].

Axiom: baa=c.

Defines rule #3.

Referenced by [3], [5], [6], [9].

Simplify [1] ababbba=baa.

Reduce RHS:

Defines rule #11.

Referenced by [4], [5], [6], [7], [8].

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

Critical pair: ababbbc=cbabbba.

Flip LHS and RHS.

Referenced by [6], [13].

Overlap of [3] ababbba=c with [2] baa=c:

Critical pair: ababbc=ca.

Defines rule #1.

Referenced by [7], [10].

Overlap of [2] baa=c with [3] ababbba=c:

Critical pair: bac=cbabbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8], [9], [11], [13], [14].

Overlap of [3] ababbba=c with [5] ababbc=ca:

Critical pair: ababbbca=cbabbc.

Reduce LHS:

Defines rule #5.

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

Overlap of [3] ababbba=c with [6] ababbbc=bac:

Critical pair: ababbbbac=cbabbbc.

Defines rule #12.

Overlap of [2] baa=c with [6] ababbbc=bac:

Critical pair: babac=cbabbbc.

Defines rule #4.

Referenced by [12].

Overlap of [7] baca=cbabbc with [5] ababbc=ca:

Critical pair: bacca=cbabbcbabbc.

Flip LHS and RHS.

Defines rule #9.

Overlap of [7] baca=cbabbc with [6] ababbbc=bac:

Critical pair: bacbac=cbabbcbabbbc.

Flip LHS and RHS.

Defines rule #10.

Overlap of [9] babac=cbabbbc with [7] baca=cbabbc:

Critical pair: bacbabbc=cbabbbca.

Flip LHS and RHS.

Defines rule #8.

Simplify [4] cbabbba=ababbbc.

Reduce RHS:

Defines rule #6.

Referenced by [14].

Overlap of [13] cbabbba=bac with [6] ababbbc=bac:

Critical pair: cbabbbbac=bacbabbbc.

Defines rule #7.