Certificate for #1924 ⟨a, b | aaabbbaa=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: aaabbbaa=ab.

Referenced by [3].

Axiom: abbb=c.

Referenced by [3], [4].

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

Critical pair: aacaa=ab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

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

Critical pair: aacaabb=c.

Reduce LHS:

Defines rule #3.

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

Overlap of [4] aacaaacaaacaa=c with [3] ab=aacaa:

Critical pair: aacaaacaaacaaacaa=cb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] aacaaacaaacaa=c with [4] aacaaacaaacaa=c:

Critical pair: aacac=cacaa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [8].

Overlap of [4] aacaaacaaacaa=c with [4] aacaaacaaacaa=c:

Critical pair: aacaaacaaacc=ccaaacaaacaa.

Flip LHS and RHS.

Defines rule #2.

Simplify [5] cb=cacaa.

Reduce RHS:

Defines rule #5.