Certificate for #2423 ⟨a, b | aaabaa=aaba⟩

Completion settings:

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

Axiom: aaabaa=aaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #5.

Referenced by [3], [4], [6], [7], [8].

Simplify [1] aaabaa=aaba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabaa=c with [2] aaba=c:

Critical pair: aca=c.

Defines rule #1.

Referenced by [5], [7], [9], [11].

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

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [2] aaba=c with [2] aaba=c:

Critical pair: aabc=caba.

Flip LHS and RHS.

Referenced by [10].

Overlap of [2] aaba=c with [4] aca=c:

Critical pair: aabc=cca.

Reduce RHS:

Defines rule #6.

Referenced by [8], [10].

Overlap of [2] aaba=c with [7] aabc=acc:

Critical pair: aabacc=cabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [9].

Overlap of [4] aca=c with [8] cabc=ccc:

Critical pair: accc=cbc.

Flip LHS and RHS.

Defines rule #4.

Simplify [6] caba=aabc.

Reduce RHS:

Defines rule #7.

Referenced by [11].

Overlap of [4] aca=c with [10] caba=acc:

Critical pair: aacc=cba.

Flip LHS and RHS.

Defines rule #3.