Certificate for #4916 ⟨a, b | aaaaaba=aaab⟩

Completion settings:

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

Axiom: aaaaaba=aaab.

Referenced by [3].

Axiom: aaab=c.

Defines rule #6.

Referenced by [3], [4], [6].

Simplify [1] aaaaaba=aaab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaaaaba=c with [2] aaab=c:

Critical pair: aaca=c.

Defines rule #2.

Referenced by [5], [6], [7], [8].

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

Critical pair: aacc=caca.

Defines rule #1.

Referenced by [6], [8].

Overlap of [4] aaca=c with [2] aaab=c:

Critical pair: aacc=caab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7].

Overlap of [4] aaca=c with [6] caab=caca:

Critical pair: aacaca=cab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

Overlap of [4] aaca=c with [7] cab=cca:

Critical pair: aacca=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.