Certificate for #19292 ⟨a, b | aaa=a, babab=ab⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [4], [7], [8], [9].

Axiom: babab=ab.

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

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

Critical pair: baab=abab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5], [6], [8].

Overlap of [1] aaa=a with [3] abab=baab:

Critical pair: aabaab=abab.

Reduce RHS:

Referenced by [8].

Overlap of [3] abab=baab with [2] babab=ab:

Critical pair: aab=baabab.

Reduce RHS:

Flip LHS and RHS.

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

Overlap of [3] abab=baab with [3] abab=baab:

Critical pair: abbaab=baabab.

Reduce RHS:

Referenced by [9].

Overlap of [2] babab=ab with [5] babaab=aab:

Critical pair: baaab=abaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [3] abab=baab with [5] babaab=aab:

Critical pair: aaab=baabaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [9].

Overlap of [8] bbaab=ab with [8] bbaab=ab:

Critical pair: bbaaab=abbaab.

Reduce LHS:

Reduce RHS:

Defines rule #2.