Certificate for #4253 ⟨a, b | abaaabbba=ab⟩

Completion settings:

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

Axiom: abaaabbba=ab.

Referenced by [3].

Axiom: abbb=c.

Defines rule #11.

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

Overlap of [1] abaaabbba=ab with [2] abbb=c:

Critical pair: abaaca=ab.

Defines rule #6.

Referenced by [4], [5], [6], [7], [10].

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

Critical pair: abaacc=abbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

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

Critical pair: abaacab=abbaaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

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

Overlap of [3] abaaca=ab with [5] abbaaca=abb:

Critical pair: abaacabb=abbbaaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [8], [9], [12].

Overlap of [3] abaaca=ab with [6] caaca=c:

Critical pair: abaac=abaca.

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] abbaaca=abb with [6] caaca=c:

Critical pair: abbaac=abbaca.

Flip LHS and RHS.

Defines rule #9.

Overlap of [6] caaca=c with [6] caaca=c:

Critical pair: caac=caca.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [3] abaaca=ab with [9] caca=caac:

Critical pair: abaacaac=abca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [5] abbaaca=abb with [9] caca=caac:

Critical pair: abbaacaac=abbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] caaca=c with [9] caca=caac:

Critical pair: caacaac=cca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.