Certificate for #2624 ⟨a, b | abbaab=bbaa⟩

Completion settings:

• Auxiliary generators:
  1. c = bbaa
  2. d = bb
• Reduction order:
  • Left-to-right recursive path with deg(d) = deg(c) = 0, d < c; deg(a) = 1; deg(b) = 2

Axiom: abbaab=bbaa.

Referenced by [4].

Axiom: bbaa=c.

Referenced by [6].

Axiom: bb=d.

Defines rule #8.

Referenced by [4], [5], [6], [7], [9].

Simplify [1] abbaab=bbaa.

Reduce RHS:

Referenced by [5].

Overlap of [4] abbaab=daa with [3] bb=d:

Critical pair: adaab=daa.

Referenced by [8].

Overlap of [2] bbaa=c with [3] bb=d:

Critical pair: daa=c.

Defines rule #4.

Referenced by [8], [10], [13].

Overlap of [3] bb=d with [3] bb=d:

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

Simplify [5] adaab=daa.

Reduce LHS:

Reduce RHS:

Referenced by [9], [10], [11], [12].

Overlap of [8] acb=c with [3] bb=d:

Critical pair: acd=cb.

Flip LHS and RHS.

Defines rule #7.

Referenced by [10], [12].

Overlap of [6] daa=c with [8] acb=c:

Critical pair: dac=ccb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11].

Overlap of [10] cacd=dac with [7] db=bd:

Critical pair: cacbd=dacb.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [8] acb=c with [9] cb=acd:

Critical pair: aacd=c.

Defines rule #3.

Referenced by [13].

Overlap of [12] aacd=c with [6] daa=c:

Critical pair: aacc=caa.

Flip LHS and RHS.

Defines rule #5.