Certificate for #2431 ⟨a, b | aaabaa=baba⟩

Completion settings:

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

Axiom: aaabaa=baba.

Referenced by [3].

Axiom: ba=c.

Defines rule #1.

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

Simplify [1] aaabaa=baba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabaa=cc with [2] ba=c:

Critical pair: aaaca=cc.

Defines rule #7.

Referenced by [5], [6], [7], [8], [10].

Overlap of [2] ba=c with [4] aaaca=cc:

Critical pair: bcc=caaca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [8], [9], [11].

Overlap of [4] aaaca=cc with [4] aaaca=cc:

Critical pair: aaaccc=ccaaca.

Reduce RHS:

Defines rule #4.

Referenced by [10], [11].

Overlap of [4] aaaca=cc with [5] caaca=bcc:

Critical pair: aaabcc=ccaca.

Defines rule #8.

Overlap of [5] caaca=bcc with [4] aaaca=cc:

Critical pair: caaccc=bccaaca.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [5] caaca=bcc with [5] caaca=bcc:

Critical pair: caabcc=bccaca.

Defines rule #5.

Overlap of [4] aaaca=cc with [6] aaaccc=cbcc:

Critical pair: aaaccbcc=ccaaccc.

Defines rule #9.

Overlap of [5] caaca=bcc with [6] aaaccc=cbcc:

Critical pair: caaccbcc=bccaaccc.

Defines rule #6.