Certificate for #2390 ⟨a, b | aaaaba=aaab⟩

Completion settings:

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

Axiom: aaaaba=aaab.

Referenced by [3].

Axiom: aaab=c.

Defines rule #5.

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

Simplify [1] aaaaba=aaab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aca=c.

Defines rule #1.

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

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

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #2.

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

Critical pair: acc=caab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [7].

Overlap of [4] aca=c with [6] caab=acc:

Critical pair: aacc=cab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

Overlap of [4] aca=c with [7] cab=aacc:

Critical pair: aaacc=cb.

Flip LHS and RHS.

Defines rule #3.