Certificate for #4245 ⟨a, b | abaaababa=ab⟩

Completion settings:

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

Axiom: abaaababa=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #4.

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

Simplify [1] abaaababa=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: caaababa=c.

Reduce LHS:

Defines rule #3.

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

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

Critical pair: caaccc=cb.

Flip LHS and RHS.

Defines rule #5.

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

Critical pair: caacc=cacca.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [4] caacca=c with [6] cacca=caacc:

Critical pair: caaccaacc=ccca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.