Certificate for #14580 ⟨a, b | aaba=a, babab=b⟩

Completion settings:

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

Axiom: aaba=a.

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

Axiom: babab=b.

Referenced by [3], [7].

Overlap of [1] aaba=a with [2] babab=b:

Critical pair: aab=abab.

Flip LHS and RHS.

Referenced by [4], [6].

Overlap of [1] aaba=a with [3] abab=aab:

Critical pair: aaab=ab.

Referenced by [5].

Overlap of [4] aaab=ab with [1] aaba=a:

Critical pair: aa=aba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [7].

Overlap of [3] abab=aab with [5] aba=aa:

Critical pair: abaa=aaba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [2] babab=b with [5] aba=aa:

Critical pair: baab=b.

Defines rule #3.