Certificate for #2039 ⟨a, b | abaababa=ab⟩

Completion settings:

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

Axiom: abaababa=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #3.

Referenced by [3], [4], [5].

Simplify [1] abaababa=ab.

Reduce RHS:

Referenced by [4].

Overlap of [3] abaababa=c with [2] ab=c:

Critical pair: caababa=c.

Reduce LHS:

Defines rule #2.

Referenced by [5], [6].

Overlap of [4] cacca=c with [2] ab=c:

Critical pair: caccc=cb.

Flip LHS and RHS.

Defines rule #4.

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

Critical pair: cacc=ccca.

Flip LHS and RHS.

Defines rule #1.