Certificate for #9145 ⟨a, b | aa=a, abab=abb⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

Referenced by [6].

Axiom: abab=abb.

Referenced by [4].

Axiom: ab=c.

Defines rule #3.

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

Simplify [2] abab=abb.

Reduce RHS:

Referenced by [5].

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

Critical pair: cab=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

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

Critical pair: ac=ab.

Reduce RHS:

Defines rule #2.