Certificate for #1827 ⟨a, b | aaaaaaba=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: aaaaaaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #4.

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

Simplify [1] aaaaaaba=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aaaaaca=c.

Defines rule #2.

Referenced by [5], [6].

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

Critical pair: aaaaacc=cb.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: aaaaacc=caaaaca.

Defines rule #1.

Referenced by [7].

Simplify [5] cb=aaaaacc.

Reduce RHS:

Defines rule #3.