Certificate for #12466 ⟨a, b | aabb=ab, bbaa=a⟩

Completion settings:

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

Axiom: aabb=ab.

Referenced by [3], [4], [5], [9].

Axiom: bbaa=a.

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

Overlap of [1] aabb=ab with [2] bbaa=a:

Critical pair: aaa=abaa.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aabb=ab with [2] bbaa=a:

Critical pair: aaba=abbaa.

Reduce RHS:

Referenced by [6].

Overlap of [2] bbaa=a with [1] aabb=ab:

Critical pair: bbab=abb.

Referenced by [10].

Overlap of [2] bbaa=a with [4] aaba=aa:

Critical pair: bbaa=aba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [11].

Simplify [3] abaa=aaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [2] bbaa=a with [7] aaa=aa:

Critical pair: bbaa=aa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [9].

Overlap of [7] aaa=aa with [1] aabb=ab:

Critical pair: aab=aabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [10].

Simplify [5] bbab=abb.

Reduce RHS:

Referenced by [11].

Overlap of [10] bbab=ab with [6] aba=a:

Critical pair: bba=aba.

Reduce RHS:

Defines rule #4.