Certificate for #2046 ⟨a, b | abaabbba=ab⟩

Completion settings:

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

Axiom: abaabbba=ab.

Referenced by [3].

Axiom: abbb=c.

Defines rule #8.

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

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

Critical pair: abaca=ab.

Defines rule #4.

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

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

Critical pair: abacc=abbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

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

Critical pair: abacab=abbaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [6], [8].

Overlap of [3] abaca=ab with [5] abbaca=abb:

Critical pair: abacabb=abbbaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [3] abaca=ab with [6] caca=c:

Critical pair: abac=abca.

Flip LHS and RHS.

Defines rule #3.

Overlap of [5] abbaca=abb with [6] caca=c:

Critical pair: abbac=abbca.

Flip LHS and RHS.

Defines rule #6.

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

Critical pair: cac=cca.

Flip LHS and RHS.

Defines rule #1.