Certificate for #1940 ⟨a, b | aabaaaba=ab⟩

Completion settings:

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

Axiom: aabaaaba=ab.

Referenced by [3].

Axiom: aba=c.

Referenced by [3], [4].

Overlap of [1] aabaaaba=ab with [2] aba=c:

Critical pair: acaaba=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [6].

Overlap of [2] aba=c with [3] ab=acac:

Critical pair: acaca=c.

Defines rule #2.

Referenced by [5], [6].

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

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

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

Critical pair: acacacac=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.