Certificate for #5013 ⟨a, b | aaabaaa=aaba⟩

Completion settings:

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

Axiom: aaabaaa=aaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #5.

Referenced by [3], [4], [6], [7], [8], [10].

Simplify [1] aaabaaa=aaba.

Reduce RHS:

Referenced by [4].

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

Critical pair: acaa=c.

Defines rule #1.

Referenced by [5], [7], [8], [9], [10].

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

Critical pair: acac=ccaa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [9], [10].

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

Critical pair: aabc=caba.

Flip LHS and RHS.

Referenced by [10], [11].

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

Critical pair: aabc=ccaa.

Reduce RHS:

Defines rule #6.

Referenced by [11].

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

Critical pair: acc=cba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [9].

Overlap of [8] cba=acc with [4] acaa=c:

Critical pair: cbc=acccaa.

Reduce RHS:

Defines rule #4.

Overlap of [5] ccaa=acac with [2] aaba=c:

Critical pair: ccac=acacaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Simplify [6] caba=aabc.

Reduce RHS:

Defines rule #7.