Certificate for #13198 ⟨a, b | abb=aab, bab=aa⟩

Completion settings:

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

Axiom: abb=aab.

Defines rule #1.

Referenced by [4], [5], [6], [9].

Axiom: bab=aa.

Defines rule #2.

Referenced by [3], [4], [5], [7], [8].

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

Critical pair: baaa=aaab.

Referenced by [6], [7], [8], [9], [11].

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

Critical pair: abaa=aabab.

Reduce RHS:

Defines rule #4.

Referenced by [9].

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

Critical pair: baab=aab.

Defines rule #6.

Referenced by [6], [7].

Overlap of [5] baab=aab with [1] abb=aab:

Critical pair: baaab=aabb.

Reduce LHS:

Reduce RHS:

Referenced by [8], [9].

Overlap of [5] baab=aab with [2] bab=aa:

Critical pair: baaaa=aabab.

Reduce LHS:

Reduce RHS:

Referenced by [8], [9].

Overlap of [2] bab=aa with [3] baaa=aaab:

Critical pair: baaaab=aaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [3] baaa=aaab with [4] abaa=aaaa:

Critical pair: baaaaaa=aaabbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [10], [11].

Simplify [8] aaaaa=aaab.

Reduce RHS:

Defines rule #7.

Simplify [3] baaa=aaab.

Reduce RHS:

Defines rule #5.