Certificate for #15962 ⟨a, b | aaa=aa, abab=ba⟩

Completion settings:

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

Axiom: aaa=aa.

Defines rule #1.

Referenced by [3].

Axiom: abab=ba.

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

Overlap of [1] aaa=aa with [2] abab=ba:

Critical pair: aaba=aabab.

Reduce RHS:

Referenced by [5].

Overlap of [2] abab=ba with [2] abab=ba:

Critical pair: abba=baab.

Flip LHS and RHS.

Referenced by [8].

Overlap of [3] aaba=aba with [2] abab=ba:

Critical pair: aba=abab.

Reduce RHS:

Defines rule #2.

Referenced by [6], [7], [8].

Overlap of [2] abab=ba with [5] aba=ba:

Critical pair: bab=ba.

Defines rule #3.

Referenced by [7].

Overlap of [6] bab=ba with [5] aba=ba:

Critical pair: bba=baa.

Defines rule #4.

Referenced by [8].

Simplify [4] baab=abba.

Reduce RHS:

Defines rule #5.