Certificate for #3180 ⟨a, b, c | ba=ab, aabc=1⟩

Completion settings:

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

Axiom: ba=ab.

Flip LHS and RHS.

Referenced by [2], [4].

Axiom: aabc=1.

Reduce LHS:

Referenced by [5].

Axiom: ba=d.

Referenced by [4], [5], [6], [7], [9], [11].

Simplify [1] ab=ba.

Reduce RHS:

Referenced by [6], [7].

Overlap of [2] baac=1 with [3] ba=d:

Critical pair: dac=1.

Referenced by [8].

Overlap of [4] ab=d with [3] ba=d:

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [10].

Overlap of [3] ba=d with [4] ab=d:

Critical pair: bd=db.

Flip LHS and RHS.

Referenced by [12].

Overlap of [5] dac=1 with [6] da=ad:

Critical pair: adc=1.

Defines rule #2.

Referenced by [9], [10].

Overlap of [3] ba=d with [8] adc=1:

Critical pair: b=ddc.

Defines rule #6.

Referenced by [11], [12].

Overlap of [6] da=ad with [8] adc=1:

Critical pair: d=addc.

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] ba=d with [9] b=ddc:

Critical pair: ddca=d.

Defines rule #4.

Simplify [7] db=bd.

Reduce LHS:

Reduce RHS:

Defines rule #5.