Certificate for #1018 ⟨a, b | aaaaba=aab⟩

Completion settings:

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

Axiom: aaaaba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #5.

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

Simplify [1] aaaaba=aab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aaca=c.

Defines rule #2.

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

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

Critical pair: aacc=cab.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: aacc=caca.

Defines rule #1.

Referenced by [7].

Simplify [5] cab=aacc.

Reduce RHS:

Defines rule #4.

Referenced by [8].

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

Critical pair: aacaca=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.