Certificate for #470 ⟨a, b | abaaba=ab⟩

Completion settings:

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

Axiom: abaaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #4.

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

Simplify [1] abaaba=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: caaba=c.

Reduce LHS:

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

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

Critical pair: cacc=cb.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: cac=cca.

Defines rule #1.

Referenced by [7], [8].

Overlap of [4] caca=c with [6] cac=cca:

Critical pair: ccaa=c.

Defines rule #2.

Simplify [5] cb=cacc.

Reduce RHS:

Defines rule #3.