Certificate for #16186 ⟨a, b | aab=ab, baba=ab⟩

Completion settings:

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

Axiom: aab=ab.

Defines rule #1.

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

Axiom: baba=ab.

Referenced by [3], [4], [5], [7].

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

Critical pair: babab=abab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5], [6].

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

Critical pair: baab=abba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5].

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

Critical pair: aab=abba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7].

Overlap of [1] aab=ab with [5] bab=ab:

Critical pair: aaab=abab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [2] baba=ab with [5] bab=ab:

Critical pair: aba=ab.

Defines rule #2.