Certificate for #4066 ⟨a, b | aabaaaaba=ab⟩

Completion settings:

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

Axiom: aabaaaaba=ab.

Referenced by [3].

Axiom: aaba=c.

Referenced by [3], [4].

Overlap of [1] aabaaaaba=ab with [2] aaba=c:

Critical pair: caaaba=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

Overlap of [2] aaba=c with [3] ab=cac:

Critical pair: acaca=c.

Defines rule #2.

Referenced by [5], [6].

Overlap of [4] acaca=c with [3] ab=cac:

Critical pair: acaccac=cb.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

Simplify [5] cb=acaccac.

Reduce RHS:

Defines rule #4.