Certificate for #18697 ⟨a, b | aaa=a, aaabaa=b⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #2.

Referenced by [2], [3], [4].

Axiom: aaabaa=b.

Reduce LHS:

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

Overlap of [1] aaa=a with [2] abaa=b:

Critical pair: aab=abaa.

Reduce RHS:

Referenced by [5].

Overlap of [2] abaa=b with [1] aaa=a:

Critical pair: aba=ba.

Referenced by [6].

Overlap of [3] aab=b with [2] abaa=b:

Critical pair: ab=baa.

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [2] abaa=b with [4] aba=ba:

Critical pair: baa=b.

Reduce LHS:

Defines rule #1.

Referenced by [7].

Simplify [5] baa=ab.

Reduce RHS:

Defines rule #3.