Certificate for #16170 ⟨a, b | aab=ab, abba=ab⟩

Completion settings:

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

Axiom: aab=ab.

Defines rule #1.

Referenced by [3].

Axiom: abba=ab.

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

Overlap of [2] abba=ab with [1] aab=ab:

Critical pair: abbab=abab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [2] abba=ab with [3] abab=abb:

Critical pair: abbabb=abbab.

Reduce LHS:

Reduce RHS:

Referenced by [5].

Overlap of [3] abab=abb with [2] abba=ab:

Critical pair: abab=abbba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [6].

Overlap of [2] abba=ab with [5] abb=ab:

Critical pair: aba=ab.

Defines rule #2.