Certificate for #4598 ⟨a, b | aabaaaba=aab⟩

Completion settings:

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

Axiom: aabaaaba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #5.

Referenced by [3], [4], [5], [8].

Simplify [1] aabaaaba=aab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aabaaaba=c with [2] aab=c:

Critical pair: caaaba=c.

Reduce LHS:

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

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

Critical pair: cacc=cab.

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: cac=cca.

Defines rule #1.

Referenced by [7], [9].

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

Critical pair: ccaa=c.

Defines rule #2.

Referenced by [8].

Overlap of [7] ccaa=c with [2] aab=c:

Critical pair: ccc=cb.

Flip LHS and RHS.

Defines rule #3.

Simplify [5] cab=cacc.

Reduce RHS:

Defines rule #4.