Certificate for #19811 ⟨a, b | aaa=a, abab=bab⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #3.

Referenced by [7].

Axiom: abab=bab.

Referenced by [4].

Axiom: ab=c.

Defines rule #1.

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

Simplify [2] abab=bab.

Reduce RHS:

Referenced by [5].

Overlap of [4] abab=bc with [3] ab=c:

Critical pair: cab=bc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

Overlap of [3] ab=c with [5] bc=cc:

Critical pair: acc=cc.

Defines rule #5.

Overlap of [1] aaa=a with [3] ab=c:

Critical pair: aac=ab.

Reduce RHS:

Defines rule #4.