Certificate for #25237 ⟨a, b | aa=a, babab=abb⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

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

Axiom: babab=abb.

Defines rule #5.

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

Overlap of [2] babab=abb with [2] babab=abb:

Critical pair: baabb=abbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4], [5], [7], [10].

Overlap of [1] aa=a with [3] abbab=babb:

Critical pair: ababb=abbab.

Reduce RHS:

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

Overlap of [3] abbab=babb with [2] babab=abb:

Critical pair: ababb=babbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] babab=abb with [4] ababb=babb:

Critical pair: bbabb=abbb.

Reduce LHS:

Defines rule #2.

Referenced by [7], [8], [10].

Overlap of [4] ababb=babb with [3] abbab=babb:

Critical pair: abbabb=babbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] babab=abb with [6] babb=abbb:

Critical pair: baabbb=abbb.

Reduce LHS:

Defines rule #4.

Referenced by [9].

Simplify [7] abbbab=abbbb.

Reduce RHS:

Defines rule #6.

Simplify [3] abbab=babb.

Reduce RHS:

Defines rule #3.