Certificate for #2031 ⟨a, b | abaaabba=ab⟩

Completion settings:

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

Axiom: abaaabba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #8.

Referenced by [3], [4], [5].

Overlap of [1] abaaabba=ab with [2] abb=c:

Critical pair: abaaca=ab.

Defines rule #6.

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

Overlap of [3] abaaca=ab with [2] abb=c:

Critical pair: abaacc=abbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [3] abaaca=ab with [3] abaaca=ab:

Critical pair: abaacab=abbaaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [3] abaaca=ab with [5] caaca=c:

Critical pair: abaac=abaca.

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] caaca=c with [5] caaca=c:

Critical pair: caac=caca.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9].

Overlap of [3] abaaca=ab with [7] caca=caac:

Critical pair: abaacaac=abca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [5] caaca=c with [7] caca=caac:

Critical pair: caacaac=cca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.