Certificate for #19267 ⟨a, b | aaa=a, ababa=ab⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b

Axiom: aaa=a.

Defines rule #1.

Referenced by [3].

Axiom: ababa=ab.

Referenced by [3], [4], [5], [6].

Overlap of [2] ababa=ab with [1] aaa=a:

Critical pair: ababa=abaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

Overlap of [2] ababa=ab with [2] ababa=ab:

Critical pair: abab=abba.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] ababa=ab with [3] abaa=ab:

Critical pair: abab=aba.

Defines rule #4.

Referenced by [6].

Overlap of [3] abaa=ab with [2] ababa=ab:

Critical pair: abaab=abbaba.

Reduce LHS:

Reduce RHS:

Defines rule #2.