Certificate for #16194 ⟨a, b | aab=ab, bbaa=ab⟩

Completion settings:

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

Axiom: aab=ab.

Defines rule #1.

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

Axiom: bbaa=ab.

Defines rule #5.

Referenced by [3], [4], [6], [7].

Overlap of [2] bbaa=ab with [1] aab=ab:

Critical pair: bbab=abb.

Referenced by [5], [8].

Overlap of [2] bbaa=ab with [1] aab=ab:

Critical pair: bbaab=abab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5], [6], [7], [9].

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

Critical pair: ababb=abbab.

Reduce LHS:

Reduce RHS:

Referenced by [6], [7].

Overlap of [5] abbb=abb with [2] bbaa=ab:

Critical pair: abab=abbaa.

Reduce LHS:

Reduce RHS:

Defines rule #2.

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

Overlap of [5] abbb=abb with [2] bbaa=ab:

Critical pair: abbab=abbbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Simplify [3] bbab=abb.

Reduce RHS:

Defines rule #6.

Simplify [4] abab=abb.

Reduce RHS:

Defines rule #4.