Certificate for #14721 ⟨a, b | aabb=a, bbbaa=a⟩

Completion settings:

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

Axiom: aabb=a.

Referenced by [3], [4], [5], [6], [7].

Axiom: bbbaa=a.

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

Overlap of [1] aabb=a with [2] bbbaa=a:

Critical pair: aaa=abaa.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] bbbaa=a with [1] aabb=a:

Critical pair: bbba=abb.

Referenced by [5], [7], [8], [9].

Overlap of [2] bbbaa=a with [1] aabb=a:

Critical pair: bbbaa=aabb.

Reduce LHS:

Reduce RHS:

Referenced by [7], [8].

Overlap of [3] abaa=aaa with [1] aabb=a:

Critical pair: aba=aaabb.

Reduce RHS:

Referenced by [7], [8], [10].

Overlap of [1] aabb=a with [4] bbba=abb:

Critical pair: aababb=abba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [8], [10].

Overlap of [4] bbba=abb with [6] aba=aa:

Critical pair: bbbaa=abbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [9].

Simplify [4] bbba=abb.

Reduce RHS:

Defines rule #4.

Simplify [6] aba=aa.

Reduce RHS:

Defines rule #2.