Certificate for #5038 ⟨a, b | aaa=aa, babb=a⟩

Completion settings:

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

Axiom: aaa=aa.

Defines rule #1.

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

Axiom: babb=a.

Defines rule #6.

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

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

Critical pair: baba=aabb.

Defines rule #3.

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

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

Critical pair: baa=aabbbb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [6].

Overlap of [3] baba=aabb with [3] baba=aabb:

Critical pair: baaabb=aabbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

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

Critical pair: abaa=aabbbb.

Reduce RHS:

Defines rule #2.

Referenced by [7].

Overlap of [3] baba=aabb with [6] abaa=baa:

Critical pair: bbaa=aabba.

Defines rule #5.

Referenced by [8].

Overlap of [2] babb=a with [7] bbaa=aabba:

Critical pair: baaabba=aaa.

Reduce LHS:

Reduce RHS:

Defines rule #8.

Referenced by [9].

Overlap of [8] baabba=aa with [2] babb=a:

Critical pair: baaba=aabb.

Defines rule #4.