Certificate for #4762 ⟨a, b | abaaaaba=aab⟩

Completion settings:

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

Axiom: abaaaaba=aab.

Referenced by [4].

Axiom: ab=c.

Defines rule #6.

Referenced by [4], [5], [8].

Axiom: aaac=d.

Referenced by [5], [6].

Simplify [1] abaaaaba=aab.

Reduce RHS:

Referenced by [5].

Overlap of [4] abaaaaba=ac with [2] ab=c:

Critical pair: caaaaba=ac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [9], [10].

Overlap of [3] aaac=d with [5] ac=cda:

Critical pair: aacda=d.

Reduce LHS:

Defines rule #4.

Referenced by [7], [8], [9], [14].

Overlap of [5] ac=cda with [6] cdadada=d:

Critical pair: ad=cdadadada.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11], [13], [15].

Overlap of [6] cdadada=d with [2] ab=c:

Critical pair: cdadadc=db.

Flip LHS and RHS.

Referenced by [12].

Overlap of [6] cdadada=d with [5] ac=cda:

Critical pair: cdadadcda=dc.

Referenced by [14].

Overlap of [7] dda=ad with [5] ac=cda:

Critical pair: ddcda=adc.

Flip LHS and RHS.

Referenced by [11], [12], [14].

Overlap of [7] dda=ad with [10] adc=ddcda:

Critical pair: ddddcda=addc.

Flip LHS and RHS.

Referenced by [13], [15].

Simplify [8] db=cdadadc.

Reduce RHS:

Referenced by [15].

Overlap of [7] dda=ad with [11] addc=ddddcda:

Critical pair: ddddddcda=adddc.

Flip LHS and RHS.

Referenced by [14].

Simplify [9] cdadadcda=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [15].

Simplify [12] db=cdadddcda.

Reduce RHS:

Defines rule #5.