Certificate for #3960 ⟨a, b | aaabaaaba=ab⟩

Completion settings:

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

Axiom: aaabaaaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #4.

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

Simplify [1] aaabaaaba=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aacaaaba=c.

Reduce LHS:

Defines rule #2.

Referenced by [5], [6].

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

Critical pair: aacaacc=cb.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: aacc=caca.

Defines rule #1.

Referenced by [7].

Simplify [5] cb=aacaacc.

Reduce RHS:

Defines rule #3.