Certificate for #19287 ⟨a, b | aaa=a, baabb=aa⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Axiom: aaa=a.

Defines rule #4.

Referenced by [3], [4], [6], [7], [9], [10].

Axiom: baabb=aa.

Referenced by [3], [4], [5], [8], [9].

Overlap of [2] baabb=aa with [2] baabb=aa:

Critical pair: baabaa=aaaabb.

Reduce RHS:

Referenced by [4].

Overlap of [3] baabaa=aabb with [2] baabb=aa:

Critical pair: baaaa=aabbbb.

Reduce LHS:

Defines rule #3.

Referenced by [5], [6].

Overlap of [2] baabb=aa with [4] baa=aabbbb:

Critical pair: aabbbbbb=aa.

Referenced by [10].

Overlap of [4] baa=aabbbb with [1] aaa=a:

Critical pair: ba=aabbbba.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [1] aaa=a with [6] aabbbba=ba:

Critical pair: aaba=aabbbba.

Reduce RHS:

Defines rule #5.

Overlap of [2] baabb=aa with [6] aabbbba=ba:

Critical pair: bba=aabba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [9].

Overlap of [2] baabb=aa with [8] aabba=bba:

Critical pair: bbba=aaa.

Reduce RHS:

Defines rule #2.

Overlap of [1] aaa=a with [5] aabbbbbb=aa:

Critical pair: aaa=abbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.