Certificate for #3940 ⟨a, b | abab=ba, abba=1⟩

Completion settings:

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

Axiom: abab=ba.

Defines rule #4.

Referenced by [4], [5].

Axiom: abba=1.

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

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

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [1] abab=ba with [1] abab=ba:

Critical pair: abba=baab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] abab=ba with [2] abba=1:

Critical pair: ab=baba.

Flip LHS and RHS.

Defines rule #5.

Overlap of [4] baab=1 with [4] baab=1:

Critical pair: baa=aab.

Defines rule #1.

Referenced by [7].

Overlap of [3] bba=abb with [6] baa=aab:

Critical pair: baab=abba.

Reduce LHS:

Reduce RHS:

Defines rule #3.