Certificate for #990 ⟨a, b | ababbba=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: ababbba=ab.

Referenced by [3].

Axiom: abbb=c.

Defines rule #5.

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

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

Critical pair: abca=ab.

Defines rule #2.

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

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

Critical pair: abcc=abbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: abcab=abbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [6].

Overlap of [3] abca=ab with [5] abbca=abb:

Critical pair: abcabb=abbbca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.