Certificate for #13182 ⟨a, b | abb=aaa, bab=aa⟩

Completion settings:

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

Axiom: abb=aaa.

Flip LHS and RHS.

Referenced by [3].

Axiom: bab=aa.

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [1] aaa=abb with [2] aa=bab:

Critical pair: baba=abb.

Defines rule #4.

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

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

Critical pair: abab=baba.

Reduce RHS:

Defines rule #6.

Referenced by [6], [7], [8].

Overlap of [3] baba=abb with [2] aa=bab:

Critical pair: babbab=abba.

Referenced by [6].

Overlap of [2] aa=bab with [4] abab=abb:

Critical pair: aabb=babbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [3] baba=abb with [4] abab=abb:

Critical pair: babb=abbb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9].

Overlap of [2] aa=bab with [7] abbb=babb:

Critical pair: ababb=babbbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [6] abba=babbb.

Reduce RHS:

Defines rule #5.