Certificate for #1909 ⟨a, b | aaabbaaa=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: aaabbaaa=ab.

Referenced by [3].

Axiom: abb=c.

Referenced by [3], [4].

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

Critical pair: aacaaa=ab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

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

Critical pair: aacaaab=c.

Reduce LHS:

Defines rule #3.

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

Overlap of [4] aacaaaacaaa=c with [3] ab=aacaaa:

Critical pair: aacaaaacaaaacaaa=cb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aacaac=cacaaa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [8].

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

Critical pair: aacaaaacac=ccaaaacaaa.

Flip LHS and RHS.

Defines rule #2.

Simplify [5] cb=cacaaa.

Reduce RHS:

Defines rule #5.