Certificate for #12517 ⟨a, b | abab=aa, bbbb=b⟩

Completion settings:

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

Axiom: abab=aa.

Defines rule #2.

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

Axiom: bbbb=b.

Defines rule #3.

Referenced by [4].

Overlap of [1] abab=aa with [1] abab=aa:

Critical pair: abaa=aaab.

Defines rule #1.

Referenced by [5], [6], [7].

Overlap of [1] abab=aa with [2] bbbb=b:

Critical pair: abab=aabbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [3] abaa=aaab with [1] abab=aa:

Critical pair: abaaa=aaabbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [3] abaa=aaab with [3] abaa=aaab:

Critical pair: abaaaab=aaabbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [3] abaa=aaab with [4] aabbb=aa:

Critical pair: abaaa=aaababbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [8].

Simplify [6] aaabbaa=aaaaabb.

Reduce RHS:

Defines rule #6.