Certificate for #3808 ⟨a, b | abbaababba=b⟩

Completion settings:

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

Axiom: abbaababba=b.

Referenced by [3].

Axiom: babba=c.

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

Overlap of [1] abbaababba=b with [2] babba=c:

Critical pair: abbaac=b.

Referenced by [4], [6].

Overlap of [2] babba=c with [3] abbaac=b:

Critical pair: bb=cac.

Referenced by [5], [6].

Overlap of [2] babba=c with [4] bb=cac:

Critical pair: bacaca=c.

Referenced by [7].

Overlap of [3] abbaac=b with [4] bb=cac:

Critical pair: acacaac=b.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7].

Simplify [5] bacaca=c.

Reduce LHS:

Defines rule #4.

Referenced by [8], [9], [10].

Overlap of [7] acacaacacaca=c with [7] acacaacacaca=c:

Critical pair: acacaacc=cacacaca.

Defines rule #1.

Overlap of [7] acacaacacaca=c with [7] acacaacacaca=c:

Critical pair: acacaacacc=ccaacacaca.

Defines rule #2.

Overlap of [7] acacaacacaca=c with [7] acacaacacaca=c:

Critical pair: acacaacacacc=ccacaacacaca.

Defines rule #3.