Certificate for #5628 ⟨a, b, c | aa=a, abc=ba⟩

Completion settings:

• Auxiliary generators:
  1. d = ab
• Reduction order:
  • Left-to-right shortlex with a < d < b < c

Axiom: aa=a.

Defines rule #1.

Referenced by [5].

Axiom: abc=ba.

Referenced by [4].

Axiom: ab=d.

Defines rule #3.

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

Overlap of [2] abc=ba with [3] ab=d:

Critical pair: dc=ba.

Flip LHS and RHS.

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

Overlap of [1] aa=a with [3] ab=d:

Critical pair: ad=ab.

Reduce RHS:

Defines rule #2.

Referenced by [6].

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

Critical pair: adc=da.

Reduce LHS:

Defines rule #4.

Referenced by [7], [8].

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

Critical pair: bd=dcb.

Reduce RHS:

Defines rule #6.

Simplify [4] ba=dc.

Reduce RHS:

Defines rule #5.