Certificate for #12614 ⟨a, b | baab=aa, babb=a⟩

Completion settings:

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

Axiom: baab=aa.

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

Axiom: babb=a.

Defines rule #1.

Referenced by [3], [4], [5], [6], [8].

Overlap of [2] babb=a with [2] babb=a:

Critical pair: baba=aabb.

Defines rule #4.

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

Overlap of [2] babb=a with [1] baab=aa:

Critical pair: babaa=aaab.

Reduce LHS:

Defines rule #6.

Referenced by [5], [8].

Overlap of [2] babb=a with [3] baba=aabb:

Critical pair: babaabb=aaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [3] baba=aabb with [2] babb=a:

Critical pair: baa=aabbbb.

Defines rule #3.

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

Overlap of [1] baab=aa with [6] baa=aabbbb:

Critical pair: aabbbbb=aa.

Defines rule #2.

Referenced by [8].

Overlap of [6] baa=aabbbb with [7] aabbbbb=aa:

Critical pair: baaa=aabbbbabbbbb.

Reduce LHS:

Reduce RHS:

Defines rule #8.

Referenced by [9].

Overlap of [1] baab=aa with [8] aabbbba=aaabb:

Critical pair: baaabb=aabbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.